Question

A triangle has sides of length 6cm 8cm and 10cm .the area of the circle inscribed in the triangle is.

• A. undefined
• B. undefined
• C. undefined
• D. undefined

Answer 1

A triangle of sides 6, 8 and 10 cm is clearly a right-angled triangle, since 6, 8 and 10 are pythagorean triples.
The radius of in-circle is given by $\frac{1}{2}\times (b+a-c)$, where c is the hypotenuse and a & b are sides. This can be proved as follows:


In the given problem a = 8 cm, b= 6 cm and c=10 cm
Therefore, the radius = $\frac{1}{2}\times (8+6-10)=2cm$
$\to$ Area of incircle = $\pi \times 2^2=4\pi sq.cm$