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


1

143

April 9, 2019

Prove that BP = BQ


1

124

April 9, 2019

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


1

93

April 9, 2019

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


1

255

April 9, 2019

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


1

128

April 9, 2019

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


1

290

April 9, 2019

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


1

106

April 9, 2019

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


1

107

April 9, 2019

Find the radius of the circle


1

101

April 9, 2019

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


1

297

April 9, 2019

Prove that a cyclic parallelogram is a rectangle


1

391

April 9, 2019

Prove that ∠CAD = ∠CBD


1

235

April 9, 2019

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


1

154

April 9, 2019

Prove that ∠ ACP = ∠QCD


1

110

April 9, 2019

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


1

257

April 9, 2019

If diagonals of a cyclic quadrilateral are diameters of the circle


1

270

April 9, 2019

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


1

368

April 9, 2019

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


1

100

April 9, 2019

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


1

340

April 9, 2019

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


1

325

April 9, 2019

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


1

277

April 9, 2019

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


1

96

April 9, 2019

Find the length of the string of each phone


1

345

April 9, 2019

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


1

574

April 9, 2019

Prove that AB = CD


1

158

April 9, 2019

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


1

126

April 9, 2019

If two equal chords of a circle intersect within the circle


1

166

April 9, 2019

Find the length of the common chord


1

105

April 9, 2019

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


1

471

April 9, 2019

Draw different pairs of circles


1

289

April 9, 2019
