Question

Two chords AB and CD of length 5cm and 11cm are parallel and on same side of centre. If distance between them is 3cm. Find radius of circle

Answer 1

draw OM perpendicular to AB and ON perpendicular to CD.

therefore, points M,O and N are collinear. so, MN = 6cm

Let, OM = x cm. then, ON is (6 - x) cm
join OA and OC. Then OA = OC = radius

Therefore, AM = BM = 1/2 AB = 1/2 * 5 = 2.5 cm
CN = DN = 1/2 CD = 1/2 * 11 = 5.5 cm

We also know that,
${OA}^{2} = {om}^{2} + {am}^{2}$
${OC}^{2} = {on}^{2} + {CN}^{2}$
${r}^{2} = {x}^{2} + {( \frac{5}{2} )}^{2}$
${r}^{2} = {(6 - x)}^{2} + {( \frac{11}{2} )}^{2}$
Equate both the variables - in each case it is 'r'.
Find the value of 'x' and substitute it in the formula.
Find the value of 'r' and that will be the radius.