Question

A right angled Δ ABC is inscribed in a circle , if the radius of the semicircle is 3 cm and the altitude BD
drawn to the hypotenuse is 2 cm. Then the area of the right angled Δ ABC is

Answer 1

Given : A right angled Δ ABC is inscribed in a circle , radius of the semicircle is 3 cm  altitude BD  drawn to the hypotenuse is 2 cm

To find : area of the right angled Δ ABC

Solution:

right angled Δ ABC is inscribed in a circle

=> hypotenuse AC of triangle will be diameter of circle

Radius of circle = 3cm

=> Diameter of circle = 2 * radius = 2 * 3 = 6 cm

=> AC = 6 cm

BD ⊥ AC

=> area of triangle ABC =  (1/2) * AC * BD

= (1/2) * 6  * 2

= 6

area of the right angled Δ ABC = 6 cm²

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