Question

The two circles with their centres at P and Q intersect each other. at the points A and
B. Through the point A, a straight line parallel to PQ intersects the two circles at the
points C and D respectively. If PQ = 5 cm., then let us determine the length of CD.​

Answer 1

Answer:

A).....................

Answer 2

Given: PQ = 5cm, CD is parallel to PQ, Two Circles with centers P and Q intersect at point A and B.

Construction: EF and FQ are Perpendicular bisector drawn from P and Q Respectively.

The Perpendicular from The Centre to the chord, bisects the chord.

⇒ DE = EA

⇒ CF = AF

⇒ DE + EA + AF + FC = DC

⇒ 2EA + 2AF = DC

⇒ 2(EA + AF) = DC ………..(1)

EFPQ (Given)

PEA = 90o (Construction)

QFA = 90o (Construction)

Using Interior Angle Theorem,

PEA + BPE = 180

BPE = 90o

PQFE is a rectangle.

So, EF = PQ …………… (2)

⇒ 2(EA + AF) = DC

⇒ 2EF = DC

⇒ 2PQ = CD

CD = 10cm