Q. 173.8( 12 Votes )

Prove that the ar

Answer :

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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