Question

If AB is a chord of length 24cm of a circle with centre O and radius 13cm, then find the
the distance of the chord from the centre.

Answer 1

Answer:

GIVEN: A circle with centre O, Radius AO = 13 cm, Chord AB = 24 cm

TO FIND : The perpendicular distance of the chord from O. Let it be called OM.

OM is perpendicular to the chord AB.

Perpendicular from the centre O to a chord bisects the chord.

So AM = AB/2 = 12 cm

In right triangle AMO , Using Pythagoras’s Theorem,

AO² = AM² + OM²

=> 13² = 12² + OM²

=> 169 = 144 + OM²

=> OM² = 169 - 144 = 25

=> OM = √25 = 5 cm.