Example 2

Example 2. In the adjoining figure, AB is a Chord of a circle with centre O. AB is produced to C such that BC = OB. CO is joined and produced to meet the circle to D. If Prove that x = 3y

Solution:- In (given)

[Angle opposite to equal side]

[Exterior angle is equal to sum of interior opposite angle]

Or,

in

OA = OB (radii)

[angle opposite to equal side]

= 2y

Q1. If two circles intersect each other at two points, prove that the line joining their centres is the perpendicular bisector of their common chord.

Q2. Two chords AB and AC of a circle are equal. Prove that the bisector of LBAC passes through the centre of the circle.

Q3. In the adjoining figure, l inter intersects two concentric circles with common centre O at A, B, C and D. prove that AB = CD.

Q4. In the adjoining figure, O is the centre of the circle of radius 5cm. AB = 6cm, CD = 8cm. Determine PQ

Q5. In the adjoining figure, of a circle with centre O. If BC is a diameter, prove that CA = 20D.

Answers

Equal chords of a circle are equidistant from the centre.

Chords of a circle that are equidistant from the centre are equal.