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
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
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