A chord of length 32 cm is drawn at a distance of 12 cm from the centre of a circle. Find the radius of the circle.

Question

Accepted Answer

Given:
- Length of chord (AB) = 32 cm
- Distance from centre to chord (OM) = 12 cm

Let the radius of the circle be r.

Step 1: The perpendicular from the centre of the circle to the chord bisects the chord.
So, AM = MB = 32/2 = 16 cm.

Step 2: In right triangle OMA,
OM = 12 cm (perpendicular distance from centre to chord)
AM = 16 cm (half chord length)
OA = r (radius)

Using Pythagoras theorem:
OA^2 = OM^2 + AM^2
r^2 = 12^2 + 16^2
r^2 = 144 + 256
r^2 = 400
r = √400 = 20 cm

Therefore, the radius of the circle is 20 cm.

Answer

Answer

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