In any ∆ ABC, if the angle bisector of ∠A and perpendicular bisector of BC intersect


1

844

April 9, 2019

Prove that BP = BQ


1

395

April 9, 2019

Bisectors of angles A, B and C of a ∆ABC intersect its circumcircle at D, E and F


1

415

April 9, 2019

AC and BD are chords of a circle which bisect each other


1

1110

April 9, 2019

The circle through A, B and C intersect CD at E. Prove that AE = AD


1

855

April 9, 2019

Prove that the circle drawn with any side of a rhombus as diameter


1

976

April 9, 2019

Prove that ∠ABC is equal to half the difference of the angles subtended by the chords


1

428

April 9, 2019

What is the distance of the other chord from the centre?


1

389

April 9, 2019

Find the radius of the circle


1

336

April 9, 2019

Prove that the line of centres of two intersecting circles subtends equal angles


1

997

April 9, 2019

Prove that a cyclic parallelogram is a rectangle


1

2283

April 9, 2019

Prove that ∠CAD = ∠CBD


1

876

April 9, 2019

Prove that the point of intersection of these circles lie on the third side


1

713

April 9, 2019

Prove that ∠ ACP = ∠QCD


1

427

April 9, 2019

If the nonparallel sides of a trapezium are equal, prove that it is cyclic


1

1451

April 9, 2019

If diagonals of a cyclic quadrilateral are diameters of the circle


1

1385

April 9, 2019

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E


1

1898

April 9, 2019

AC and BD intersect at a point E such that ∠ BEC = 130° and ∠ ECD = 20°. Find ∠BAC


1

468

April 9, 2019

In figure, ∠ABC = 69°,∠ACB = 31°, find ∠BDC


1

2314

April 9, 2019

In figure, ∠PQR = 100°, where P, Q and R are points on a circle with centre O. Find ∠OPR


1

1871

April 9, 2019

Find the angle subtended by the chord at a point on the minor arc


1

1417

April 9, 2019

If D is a point on the circle other than the arc ABC, find ∠ ADC


1

382

April 9, 2019

Find the length of the string of each phone


1

1280

April 9, 2019

Three girls are playing a game by standing on a circle of radius 5m drawn in a park


1

1459

April 9, 2019

Prove that AB = CD


1

968

April 9, 2019

Prove that the line joining the point of intersection to the centre


1

548

April 9, 2019

If two equal chords of a circle intersect within the circle


1

689

April 9, 2019

Find the length of the common chord


1

496

April 9, 2019

Suppose you are given a circle. Give a construction to find its centre


1

1197

April 9, 2019

Draw different pairs of circles


1

1153

April 9, 2019
