Question

students of a school were asked to make banners to promote girl education in such a way that q and r are the centres of tow congruent circles intersecting each other at point c and d. the line jioning there centres intersects the circle in point a and b such that a and b do not lie between q and r. if cd=6cm and ab =12 cm, determine the radius of either circle and the distance between the centres of two circles.

Answer 1

Let the radii of two circles be R cm.

Let the line aqOrb joining the two centers q and r intersect common chord cd at O.  The common chord and line joining centers are bisected by each other.

   So  aO = ob = ab/2 = 12/2 = 6 cm
        cO = Od = cd/2 = 6/2 = 3 cm
        oq = or = ao - R = 6 - R  cm

Δocq and Δocr are right angled.
       cr² = co² + or²
       R² = 3² + (6-R)² = 9 + 36 + R² - 12 R

=>        R = 15/4 cm
Distance between two centers = qr = ab - 2 * R = 12 - 2*15/4 = 4.5 cm