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Syllabus

The angle subtended by an arc at the centre of a circle is double the angle subtended by it at any point on the remaining part of the circle.give me the proof of this theorem !??^{0}). Sakshi calculated angle BAC as (a + 25^{0}).1) Is her finding correct? justify it.

2) Find angle BAC, If a = 30

^{0}.if two non parallel sides of a trapezium are equal prove that it is cyclic

Find the area of a cyclic quadrilateral whose sides are 8 cm,10 cm,12 cm and 16 cm.

A- ROOT 15015

B- root 30030

C-root 10010

D- none of these

PLZ SHOW THE ENTIRE WORKING

Prove that the quadrilateral formed by internal angle bisectors of a cyclic quadrilateral is also cyclic.

Two chords AB and CD of a circle intersect at right angles. If angle ABD = 65 degrees find the measure of angle CAB.

AB and CD are two parallel chords of a circle such that AB = 10cm and CD = 24. The chords are on opposite sides of the centre and distance between them is17cm. Find the radius of the circle

Prove that angles in the same segment of a circle are equal

In a circle of radius 5 cm,AB and AC are two chords such that AB = AC = 6 cm.Find the length of chord BC.

PQR is an isosceles triangle inscribed in a circle.If PQ = PR = 25cm and QR = 14, Calculate the radius of the cirlce to the neareast cm.

A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed and David re sitting at equal distance on its boundary each having a toy telephone in their hand to talk each other. Find the length of the string of each phone....This is a text ques. (Exrcise. 10.4 ques no. 6) Any one plz help me to answer this!

three students Priyanka,Sania and David are protesting against killing innocent animals for commercial purposes in a circular park of radius 20m,they are standing at equal distances on its boundary by holding banners in their hands.

Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5 m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is 6 m each, what is the distance between Reshma and Mandip?

[{i have read the solution for this but i am not understanding}]find the area of the shaded region in figure , if BC=BD=8cm,AC=AD=15cm and O is the centre of the circle.

If P, Q and R are mid points of sides BC, CA and AB of a triangle ABC, and Ad is the perpendicular from A on BC, prove that P, Q , R and D are concyclic.

plzz solve urgently!!!!

Prove that The sum of either pair of opposite angles of a cyclic

quadrilateral is 180º.

(i) $PM\perp AB\phantom{\rule{0ex}{0ex}}$

(ii) PM produced will pass through the centre O;

(iii) PM produced will bisect the major arc AB.

Two chords AB and CD of lengths 5 cm 11cm respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between AB and CD is 6 cm, find the radius of the circle.

two circle of radii 5cm and 3cm intersect at two points and the distance between their centres is 4 cm .find the length of common chord.two chord AB and AC of a circle are equal.prove that the bisector of angle BAC passes through the centre O of the circle

what is the difference between concyclic and cyclic quadrilaterals?

AB ia a diameter of the circle,CD is a chord equal to the radius of the circle.AC and BD when extended intersect t a point E. Prove that angle AEB=60 DEGREE.

2. angle PRS

3. angle PSR

4. angle PQT

ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If angleDBC = 55° and angle BAC = 45°, find BCD.

AB is a chord of a circle with radius ‘r’. If P is any point on the circle such that ∠APB is a right angle , then AB is equal to ??

how to solve this question & plz tell the method for solving

If two circles intersect at two points, then prove that their centres lie on the perpendicular bisector of the common chord.

In a circle with centre O,chords AB and CD intersect inside the circumference at E.Prove that ∠AOC + ∠BOD = 2∠AEC

ABC is a right angle triangle, right angled at A. A circle is inscribed in it. The length of two sides containing angle A is 12cm and 5cm find the radius.

ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠CAD = ∠CBD.

pls answer

Q. In the given figure AC = BC,$\text{\u2220}$DCA = $\text{\u2220}$ECB and $\text{\u2220}$DBC = $\text{\u2220}$EAC. Prove that DC = EC.

OD is perpendicular to chord AB of a circle whose centre is O. if BC is a diameter prove that CA=2OD

in the figure, chord AB of circle with centre O, is produced to C such that BC = OB . CO is joined and produced to meet the circle at D.If angle ACD = y and angle AOD = x,show that x = 3y.

Two congruent circles with centres P and Q .R is the mid point of PQ and ABRCD is a straight line. Prove that chord AB is equal tord CD

AB and AC are two chords of a circle of radius r such that AB = 2AC. if p and q are distances of AB and AC from the centre , prove that 4q

^{2 }= p^{2}= 3r^{2}X &Y are centres of circles of radius 9cm, 2cm and XY=17cm.Z is the centre ofcircle of radius r cm, which touches the above circle externally given that XZY=90degree. Write an equation inr and solve it for r

40. P, Q and R are on ML, NL and MN of the equilateral triangle MLN respectively. If MP : PL= NQ : QL = 1 : 2 and G is the centroid of the triangle PQL and S is the mid point of MN. Find LG : GS.(A) 2 : 3 (B) 4 : 5

(C) 3 : 4 (D) 1 : 3

(E) None of these

If two sides of a cyclic quadrilateral are parallel , prove tha the remaining two sides are equal and the diagonals are also equal

What is an intercepted arc and inscribed angle?

Prove measure of an intercepted arc is twice the measure of an inscribed angle.

Two congruent circles intersect each other at points A and B. Through A any line segment PAQ is drawn so that P, Q lie on the two circles. Prove that BP = BQ.

1.find the value k for which x=0 and y=8 is a solution of 3x-6y=k.

2.express x in terms of y if x/4-3y=7.

3.two cosecutive angle of a parallelogram (x+70) and (2x+50).what special name can you give to this parallelogram?

4.if the no. of square centimetres on the surface area of sphere is equal to the no. of cubic centimetres in its volume. what is it diameter of the sphere.

5.AB and CDare two equal chords of a circle with centre O . OP and OQ are perpendiculars on chords AB and CDrespectively. if angle POQ=100, find angle PQD.

if two intersecting chords of a circle make equal angles with the diameter passing through their point of intersection , prove that the chords are equal.

Two circles with centre A and B intersect at X and Y. PQ is a chord of one circle parallel to XY. prove that AB or AB produced bisects PQ.

Two circles whose centres are O and O' intersect at P. Through P, line "l" parallel to OO' intersecting the circles at C and D is drawn. Prove that CD=2OO'.

Define major sector and minor sector

If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.

an equilateral triangle of side 9 cm is inscribed in a circle.Find the radius of the circle

5. In the given figure, O is the centre of the circle. The angle subtended by the arc BCD at the centre is 140°. BC is produced to P, determine ∠BAD and ∠DCB.

a circle has radius root 2 cm. It is divided into 2 segments by a chord of length 2cm. proved that angle subtended by the chord at the point in measure segment is 45 degree

If two equal chords intersect within the circle,prove that the line joining the point of intersection to the centre makes equal angles with the chords.

prove that There is one and only one circle passing through 3 given non-collinear points

prove that the line joining the mid point of a chord to the center of the circle passes through the mid point of the corresponding minor arc

if the sum of a pair of opposite angles of a quadrilateral is 180o the quadrilateral is cyclic

In the given figure, O is the centre and AE is the diameter of the semicircle

ABCDE. If AB = BC and AEC = 50, then find

(a) CBE (b) CDE (c) AOB. Prove that BO||CE.

Two brothers have a triangle plot.They decide to distribute it equally amongst themselves but also want to give away a triangular part of it for charity to a school which is attached on the base side of 120m of the triangular plot

Answer the following

1] What is the area of the triangular plot if its height is 90m

2] Explain with the help of figure how of figure how could this be possible and what type of parts do the brothers get

3] What value of the two brothers is depicted here

Prove that the mid - point of the hypotenuse of a right triangle is equidistant from its vertices.Bisectors of angle A & C of a cyclic quadrilateral ABCD intersect a circle through A,B,C,D at E&F respectively. Proove that EF is the diameter of the circle.

Prove that the angle in a semi-circle is a right angle.

Q. The range of x, 32, 41 ,62, 64, and 71 is 45. Which of the following can be the value of X?

(A) 32 (B) 47

(C) 48 (D) 26

A chord of a circle is equal to the radius of the circle. Find the angle subtended by thre chord at a point on the minor arc and also at a point on the major arc.

prove that line segment joining midpoints of two equal chords of a circle makes equal angles with the chord

ABC IS A TRIANGLE IN WHICH AB=AC. P IS A POINT ON AC. THROUGH C A LINE IS DRAWN TO INTERSECT BP PRODUCED AT Q SUCH TAHT ANGLE ABQ=ANGLE ACQ. PROVE THAT

ANGLE AOC=90 DEGREES+ HALF OF ANGLE BAC.

if the sum of a pair of opposite angles of a quadrilateral is 180,then show that the quadrilateral is cyclic

If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.

I din't understand the answer give. Please explain me again! :O

In a circle of radius 5cm,PQ and RS are two chords of lengths 8cm and 6 cm respectively. Calculate the distance between the chords, if they are on:

i) the same side of the centre.

ii) Opposite sides of the centre.

prove that diameter is the longest chord in the circle

OABC is a rectangle inscribed in a quadrant of a circle of radius 25cm. Find the area of the rectangle,if OC =7cm. plz solve it.

In an isosceles triangle ABC with AB = AC a circle passing through B and C intersect the sides AB and AC at D and E respectively.Prove that DE||BC.

ABCD is a cyclic quadrilateral whose diagonals interest at E. If angle DBC = 70 , angle BAC=30

ulike model test paper 4 solutions

If two circles intersect each other, prove that the line joining their centres bisects the common chord at right angles.

Prove that equal chords of a circle subtend equal angles at the centre.

In case of a right angled triangle ,a circle drawn with hypotenuse as diameter passes through the opposite vertex

prove that bisectors of angles formed by producing opposite sides of cyclic quadrilateral (provided they are not parallel) intersect each other at right angle.

what is the difference between cyclic and concyclic quadrilateral??