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


2

109

April 9, 2019

Prove that BP = BQ


2

78

April 9, 2019

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


2

68

April 9, 2019

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


2

189

April 9, 2019

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


2

89

April 9, 2019

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


2

217

April 9, 2019

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


2

82

April 9, 2019

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


2

82

April 9, 2019

Find the radius of the circle


2

68

April 9, 2019

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


2

228

April 9, 2019

Prove that a cyclic parallelogram is a rectangle


2

195

April 9, 2019

Prove that ∠CAD = ∠CBD


2

141

April 9, 2019

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


2

115

April 9, 2019

Prove that ∠ ACP = ∠QCD


2

71

April 9, 2019

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


2

152

April 9, 2019

If diagonals of a cyclic quadrilateral are diameters of the circle


2

182

April 9, 2019

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


2

227

April 9, 2019

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


2

73

April 9, 2019

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


2

171

April 9, 2019

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


2

166

April 9, 2019

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


2

178

April 9, 2019

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


2

66

April 9, 2019

Find the length of the string of each phone


2

162

April 9, 2019

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


2

343

April 9, 2019

Prove that AB = CD


2

74

April 9, 2019

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


2

80

April 9, 2019

If two equal chords of a circle intersect within the circle


2

101

April 9, 2019

Find the length of the common chord


2

83

April 9, 2019

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


2

372

April 9, 2019

Draw different pairs of circles


2

185

April 9, 2019
