Properties of Congruent Chords - Theorem: Equal chords of a circle are equidistant from the centre.

OABC is a rhombus whose three vertices A, B and C lie on a circle with centre O. If the area of the rhombus is ${\displaystyle 32\sqrt{3} c{m}^2}$ find the radius of the circle.

In fig., chords AB and CD of a circle intersect at P. AP = 5cm, BP= 3cm and CP = 2.5cm. Determine the length of DP.

Prove that equal chords of congruent circles subtend equal angles at their center.

In fig, AB and CD are two equal chords of a circle with centre O. If M and N are the midpoints of AB and CD respectively,

prove that (a) ∠ ONM = ∠ ONM (b) ∠ AMN = ∠ CNM. 

A straight line is drawn cutting two equal circles and passing through the mid-point M of the line joining their centres O and O’

Prove that the chords AB and CD, which are intercepted by the two circles are equal.

OABC is a rhombus whose three vertices A, B and C lie on a circle with centre O. If the radius of the circle is 10 cm, find the area of the rhombus.

In the adjoining diagram, chords AB, BC and CD are equal. O is the centre of the circle. If ∠ ABC = 120°, Calculate: (i) ∠ BAC,   (ii) ∠ BEC, (iii) ∠ BED, (iv) ∠ COD

In fig. the centre of the circle is O. PQ and RS are two equal chords of the circle which , when produced , meet at T outside the circle . Prove that (a) TP = TR (b) TQ = TS.