In the adjoining figure triangle ABC, right angled at A, Semi circles are drawn on the sides of the triangle ABC. Prove that . . .

Question : In the adjoining figure triangle ABC, right angled at A, Semi circles are drawn on the sides of the triangle ABC. Prove that area of the shaded region is equal to the area of ∆ ABC.

Doubt by Muskan

Area of shaded region = Area of Two small Semicircle + Area of Triangle - Area of Bigger Semicircle.

Radius of Small Semicircles will be AB/2 and AC/2

Radius of Bigger Semi Circle will be given by using the Pythagoras Theorem

[√(AB^2 + AC^2)]/2

Put the Formulas and you will find that it should be coming equal to 1/2×AB×AC which is equal to the area of the ∆ ABC.

Full Solution is coming Soon.