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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 !??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.

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.

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}]what is the difference between concyclic and cyclic quadrilaterals?

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!!!!

draw a graph of the linear equation 2x + y =6 at what point the graph cuts the y axis?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.

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

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

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.

abcd is a cyclic quadrilateral within a circle centre o. if <obc=55 and bc=cd find <badABC 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.

Q15. In figure $\angle $ADE and $\angle $ABC differ by 15°. Find $\angle $CAE.

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

prove that :

a) angle in the major segment of a circle is acute

b) angle in the minor segment of circle is obtuse

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

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

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.

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

what is the difference between cyclic and concyclic quadrilateral??

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.

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.

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.

ABCDis a rhombus in which AC=16cm , BC=10cm . Find the length of diagonal BD.

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'.

distance of a chord AB from the centre of the circle is 4cm.if the length of a chord AB is 6cm,then find the diameter of the circle

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

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 .

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

ABC is a triangle inscribed in a circle with center O. If angle AOC = 130 and angle BOC = 150, find angle ACB.

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

i) triangle PAB is congruent to triangle PDC

ii) PA=PD and PC=PB

iii) AD||BC

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

Prove AO= 2/3 AD

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.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.

What is an intercepted arc and inscribed angle?

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

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

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.

Define major sector and minor sector

and <dab=60

^{0 what is the measure of <dba}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.

2. angle PRS

3. angle PSR

4. angle PQT

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

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

Distance of a chord AB of a circle from the center is 12cm and length of the chord is 10cm. Find the diameter of the circle.

prove that diameter is the longest chord in the circle

its radius is

a) 45m

b) 116 metre

c) 208 metre

d) 500.0 5 centimetre

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.

what is sum of either pair of opp sides

ulike model test paper 4 solutions

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

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

25. In fig.ABC,AEG and HEC are straight lines. Prove that $\text{\u2220AHEand\u2220EGC}$ are supplementary.