Question

Find the area of a right-angled triangle, the radius of whose circumcircle measures 8 cm and the altitude drawn to the hypotenuse measures 6 cm.

Answer 1

Let ABC be a right-angled triangle inside a circle having centre 'O'

Given, OA = OB = CC = 8 cm [OA, 0B and OC be the radius of circle]

Let AD be the altitude drawn from the opposite vertex to the hypotenuse

AD = 6 cm

Since, $△$ABC is a right triangle right angled at A

A circle can be drawn which passes througthe h the vertices of $△$ ABC (Angle in a semi-circle is 90${}^o$)

Now, the Area of $△$ABC = $\frac{1}{2}\times base\times height=\frac{1}{2}\times BC\times AD=\frac{1}{2}\times (OB+OC)\times AD=\frac{1}{2}\times (8+8)\times 6=\frac{1}{2}\times 16\times 6=48c{m}^2$