Prove that the ar

Let RST be a right triangle at S and RS = y, ST = x.

Three semi-circles are draw on the sides RS, ST and RT, respectively A1, A2 and A3.

To prove A3 = A1 + A2

In ∆RST,

by Pythagoras theorem,

RT2 = RS2 + ST2

= RT2 = y2 + x2

We know that,

Area of a semi-circle with radius,

Area of semi-circle drawn on RT,

Now, area of semi-circle drawn on RS,

And area of semi-circle drawn on ST,

On adding Equation (ii) and (iii), we get

A1 + A2 = A3

Hence proved.

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