Q-1 Prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection.
Solution:
Two Circles With Centres P and R
Two circles with centre P and R, intersecting each other at Q and S
Given
Two circles with centres P and R, which intersect each other at Q and S
Construction
Join PQ, PS, SR, QR.
In and
(radius of the same circle)
(radius of the same circle)
(common line)
Therefore by Side-Side-Side criterion of congruence,
Therefore, (corresponding parts of congruent triangles)
Q-2 Two chords PQ and RS of lengths 5cm and 11cm respectively of a circle are parallel to each and are on opposite sides of its centre. If the distance between PQ and RS is 6cm, find the radius of the circle
Solution:
O Is the Centre of Circle
O be the centre of circle and radius be r cm also OB⊥PQ and OA⊥RS, AB=6cm
Given,
O is the centre of the circle
And its radius be r cm
and
Construction,
Join OP and OR
Since both P and R are on the circle and O is the center,
and and , Therefore, B, O, A are collinear.
Let , since . Therefore,
Since, the perpendicular from the centre to a chord of the circle bisects the chord, therefore,
