Question

A triangle has a 60° angle, and the two adjacent sides are 12 and "12 times the square root of 3". Find the radius of a circle with the same vertex as a center, if the arc in the triangle bisects the area of the triangle.

Answer 1

The radius of a circle with the same vertex as a center is 12 units

Application of Pythagoras theorem;

To get the radius of the circle, we need to determine the diameter of the circle first:

According to SOH CAH TOA:

$sin\theta = \frac{opp}{hyp} \\sin60 = \frac{12\sqrt{3}}{hyp} \\hyp =\frac{12\sqrt{3}}{sin60} \\hyp =\frac{2\times12\sqrt{3}}{\sqrt3}} \\hyp = 24 = diameter$

Determine the radius of the circle

Radius = dismeter/2

Radius = 24/2

Radius = 12

Hence the radius of a circle with the same vertex as a center is 12 units

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