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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 !??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 non parallel sides of a trapezium are equal prove that it is cyclic

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

2 circles of radii 10cm and 6cm intersects at 2 points and the distance between their centers is 8cm.

Find the length of the common chord .

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

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

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.

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.

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!

in a circle of radius 25cm,two parallel chords of length 14cm and 48 cm respectively are drawn on the same side of the centre .find the distance between them.

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}]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!!!!

(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.

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

quadrilateral is 180º.

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.

x.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.13. Find the value of x in given figure.

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

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.

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

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

what is the difference between concyclic and cyclic quadrilaterals?

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.

IN A CYCLIC QUADRILATERAL PQRS , IF ANGLE P - ANGLE R = 50 DEGREE , FIND ANGLE P

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

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

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.

i) triangle PAB is congruent to triangle PDC

ii) PA=PD and PC=PB

iii) AD||BC

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

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

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. 60$\xb0$

2. 30$\xb0$

3. 45$\xb0$

4. 75$\xb0$

5. In the given figure BD = DC and $\angle $DBC = 15$\xb0$. Find $\angle $A.

1. 60$\xb0$

2. 30$\xb0$

3. 45$\xb0$

4. 75$\xb0$

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.

Show that the midpoints of congruent chords of a circle lie on another circle.

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'.

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

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

In the given figure, OA and OB are respectively perpendiculars to chords CD and

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

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.

Prove that the mid - point of the hypotenuse of a right triangle is equidistant from its vertices.2. angle PRS

3. angle PSR

4. angle PQT

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.

Define major sector and minor sector

To level a plot of land 96 and 80 sq.metres in area, the circumference of a roller has to roll over 352 Dm. How long is the roller

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

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.

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

prove that diameter is the longest chord in the circle

^{0}). Sakshi calculated angle BAC as (a + 25^{0}).1) Is her finding correct? justify it.

2) Find angle BAC, If a = 30

^{0}.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.

ulike model test paper 4 solutions

show that AD||CF.

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

ABCD is a cyclic quadrilateral.if AP,BP,CR and DR are the angles bisector of angle A,B,C and D respectively.then prove that angle APB + angle CRD = 180 DEGREE.

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