Question

A triangle with sides 13 cm 14 cm and 15 cm is inscribed in a circle. The radius of the circle is

Answer 1

Concept:

The relation between the inscribed triangle and the circle is given by:

R = (a b c) / 4Δ

Given:

We are given the sides of the triangle as 13 cm, 14 cm and 15 cm.

Find:

We need to find the radius of the circle.

Solution:

We have the sides of triangle as:

a = 13 cm

b = 14 cm

c = 15 cm

So, the area of triangle will be:

Area = Δ = √s( s - a)( s - b)( s - c).

s = a + b + c / 2 = (13 + 14 + 15) / 2 = 42 / 2 =21

Δ = √21( 21 - 13)( 21 - 14)( 21 - 15).

Δ = √21( 8 )( 7 )( 6 ).

Δ = √7056

Δ = 84 square units.

Now, we know that the radius of the circle in which a triangle is inscribed will be:

r = (a b c) / 4Δ

r= ( 13 × 14 × 15) / 4(84)

r = 8.125 cm.

Therefore, the radius of the circle is 8.125 cm.

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