Circles

Question 1Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common...

Question 2If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of...

Question 4If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD.

Question 5Three 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...

Question 6A circular park of radius 20 m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each...

Question 3In Fig. ∠PQR = 100°, where P, Q and R are points on a circle with centre O. Find ∠OPR.

Question 7If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.

Question 8If the non-parallel sides of a trapezium are equal, prove that it is cyclic.

Question 9Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q...

Question 10If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third...

Question 11ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠CAD = ∠CBD.

Question 12Prove that a cyclic parallelogram is a rectangle.