Question

In a circle of radius 13cm, two chords MN and JK are at a distance of 5cm from the centre. Find the measure of (MN + 2×JK)

Answer 1

Draw two radii MO and JO

Applying Pythagoras theorem:

OM${}^2$ = OP${}^2$ + MP${}^2$
13${}^2$ = 5${}^2$ + MP${}^2$
MP${}^2$ = 169 − 25 = 144
MP = 12
∴ MP = PN = 12 cm
MN = 24 cm
∴ MN = JK = 24 cm
MN + 2×JK = (24 + 48) cm = 72 cm

Answer: MN + 2×JK = 72 cm