Question

Two circles with centres O and P intersect at A and B. AB = 24 cm and the diameters are 30 cm and 26 cm. Calculate the length of OP.

Answer 1

Let AB and OP intersect at point M

∴ OM ⊥ AB and AM = MB   ...(Perpendicular drawn from centre bisects the chord)

∴ `AM = 1/2 xx AB`

∴ `AM = 1/2 xx 24`

∴ AM = 12

In ΔAOM, ∠AMO = 90°

AO² = AM² + OM²   ...(Pythagoras theorem)

(15)² = (12)² + OM²

225 = 144 + OM²

225 – 144 = OM²

81 = OM²

9 = OM   ...(1)

In ΔAPM, ∠AMP = 90°

AP² = AM² + MP²   ...(Pythagoras theorem)

(13)² = (12)² + MP²

169 = 144 + MP²

169 – 144 = MP²

25 = MP² 

5 = MP   ...(2)

OP = OM + MP   ...(O – M – P)

OP = 9 + 5   ...(From (1) and (2))

OP = 14 cm