Question

find the area of a right angle tiangle , if the radius of its circumcircle is 5cm and the altitude drawn to the hypothenuse is 4 cm

Answer 1

Assume a right triangle ABC, right angled at B. So, AC is hypotenuse & Altitude drawn from B to AC is BD= 4 cm

Circumcentre of any right triangle is the mid point of its hypotenuse. Let M be the mid point of hypotenuse AC.

So, M is the circumventre & AM = CM = circumradius = 5 cm.

Mow, area tri ( ABC) = 1/2 * AC * BD

=> area( tri ABC) = 1/2 * 10 * 4

=> area( tri ABC) = 20 cm²

Area( right triangle ABC) = 20 cm²