Question

Find the radius of the circle with chord and angle made by this chord is 60 degree and length of one chord is 8cm​

Answer 1

Step-by-step explanation:

Given,

A chord of length 8 cm subtends an angle of 60° at the centre.

Now,

AB = A'B (All the radii of the circle are equal)

Also,

∠BA'A = ∠BAA' (Angles opp. to equal sides are equal)

Now, by angle sum property, we get

∠BA’A + ∠BAA’ + ∠ABA’ = 180°

or, ∠BA’A + ∠BA’A + 60° = 180° (∠BA’A = ∠BAA’)

or, 2∠BA’A = 180° — 60°

or, 2∠BA’A = 120°

or, ∠BA’A = 120°/2

or, ∠BA’A = ∠BAA’ = 60° (∠BA’A = ∠BAA’)

Now,

ΔABA' is equilateral (All the angles are 60°)

So, AB = A'B = AA' = 8 cm

Hence, Radius = 8 cm.