Question

an equilateral triangle of side 6cm is inscribed in a circle . find the radius of the circle

Answer 1

Answer:

r = 2√3 cm

Step-by-step explanation:

In the fig in ΔABC AP and BQ are bisectiors of ∠A and ∠B

These bisectors meet at centre O

So OA=OB=r

In the Δ AOP

BP=6/2=3 cm ( As the angle bisector in equilateral triangle is bisectot and perpendicular to the opposite side BC)

Also ∠OPB=90°

So in ΔOPB

cos 30=BP/r=3/r

√3/2=3/r

r=3*2/√3=2*√3*√3/√3

r = 2√3 cm

Answer 2

Answer:

r = 2√3 m

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