Question

two circles with Centre A and B intersect at C and D. PCQ is a line parallel to AB intersecting the Circles at P and Q prove that PQ is equal to 2 AB

Answer 1

AB is a chord of circle with centre O as shown in figure.

according to question,

PQ passing through centre O. hence, PQ is a diameter of circle { as we know, a line segment passing through centre cut the circle at two points is known as diameter of circle }

so, PQ is diameter of circle and we know, half of diameter of circle is known as radius of circle. here POQ = 2AB , means Length of AB is equal to length of radius.

Let radius of circle is r

then, AB = r

from figure it is clear that OA and OB are the radius of circle .

so, OA = OB = r