Question

An isosceles triangle with equal sides of 5 inches and a base of 6 inches is inscribed in a circle. What is the radius, in inches, of the circle

Answer 1

The radius of the circle is 3.12 inch.

What is isosceles triangle?

A triangle having two sides of equal length. Additionally equal are the angles that face the equal sides. Triangle of isosceles. Having two identical sides and angles.

Calculation for the radius of the circle;

Consider the isosceles triangle ABC inscribed in a a circle (attached figure)

Sides AB = AC = 5 inches.

Side BC = 6 inches.

Join OB, OC and OA.

Draw perpendicular on BC from AD which passes from the centre O.

OD bisects BC at point D.

So, BD = DC = 3 inches.

In the right angled triangle ABC

AB² = AD² + BD²

5² = AD² + 3²

AD² = 16

AD = 4 inches.

Let the radius of the circle be r.

Then, OB = OC = OA =  r

OD = AD - AO

OD = 4 - r

In the right angled triangle OBD;

OB² = OD² + BD²

r² = (4-r)² + 3³

On solving,

r = 25/8 = 3.12

Therefore, the radius of the circle comes out to be 3.12 inches.

To know more about the isosceles triangle, here

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