In the given figure, Ab = 30 cm and CD = 24
cm. What is the value (in cm) of MN?

If we draw a perpendicular to a chord of any circle, the per divide the chord in two equal part. CD is chord for small circle and AB is chord for bigger circle.   r = small circle radius   R = bigger circle radius Apply PGT in ∆ OTC x² = (x)² – (12)² ---- (1) Apply PGT in ∆ OAP x² = (R)² – (15)² ------(2) From   (1) and (2) R2 – (15)² = r² – (12)² R2 – r² = 225 – 114 = 81 Apply PGT in ∆ OTM R2 – r² = TM² 81 = TM² TM = 9 We know OT divide chord MN in 2 equal part (TM = TN) MN = TM + TN MN = 9 + 9 = 18