Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.

3

(a)

Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points?

3

(a)

Two 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 chord.

3

(a)

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.

3

(a)

A 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 having a toy telephone in his hands to talk each other. Find the length of the string of each phone.

3

(a)

In figure, \(\angle ABC=69°,\quad \angle ACB=31°\), find \(\angle BDC\) .

3

(a)

In figure, A, B,C and Dare four points on a circle. AC an BD interest at a point E such that \(\angle BEC=130°\) and \(\angle ECD=20°\) . Find \(\angle BAC\).

3

(a)

ABCD is a cyclic quadrilateral whose diagonals interest at a point E. If \(\angle DBC=70°,\quad \angle BAC\) is 40°, find \(\angle BCD\) . Further, if AB=BC, find \(\angle ECD\) .

3

(a)

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

3

(a)

Prove that a cyclic parallelogram is a rectangle.

3

(a)

ABCD is a parallelogram. The circle through A, Band C intersect CD (produced if necessary) at E. Prove that AE = AD.

3

(a)

In the given figure, if O is the centre of circle, determine \(\angle APB\).

3

(a)

In figure, O is the centre of the circle, \(\angle CAO=40°\) and \(\angle CBO=30°\) , find x.

3

(a)

If O is the circumcentre of a \(\Delta\)ABC and OD\(\bot\) BC, then prove that \(\angle\)BOD = \(\angle\)BAC.

3

(a)

In the figure, AB and CD are two chords of a circle with centre O such that MP = NP. If OM \(\bot\) AB and ON \(\bot\)DC, show that AB = CD.

3

(a)