Question

an equilateral triangle is inscribed in a circle of radius 6 cm. Find its side.

Answer 1

Produce AO to D

Now AD becomes perpendicular to BC

As its also median for equilateral

And centre is centroid also

As centroid divides median in 2:1

So OD = 6/2 = 3

AD = 6+3 = 9

Now in ABD

AB^2 = AD^2 + BD^2

BD = (1/2 AB)

AB^2 - BD^2 = AD^2

AB^2 - AB^2/4 = 9^2

AB^2( 3/4) = 81

AB^2 = 81× 4/3 = 27 × 4

AB= 2× 3√3 = 6√3

Answer 2

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