PROVE THAT THE AREA OF THE SEMI CIRCLE DRAWN ON THE HYPOENUSE OF A RIGHT ANGLED TRIANGLE IS EQUAL TO - Maths - Triangles

Question

PROVE THAT THE AREA OF THE SEMI CIRCLE DRAWN ON THE HYPOENUSE OF
A RIGHT ANGLED TRIANGLE IS EQUAL TO THE SUM OF THE AREAS OF THE
SEMICIRCLES DRAWN ON THE OTHER TWO SIDES OF THE TRIANGLE

Sunanta Meitei · Accepted Answer

Here is the proof
Let ΔABC be right angled at B
Let AB = c, BC = a, AC = b
To prove:
Area of semi circle along AC = Area of semi circle along AB +
Area of semi circle along BC
<img alt="" height="340" src=
"https://s3mn%20mnimgs%20com/img/shared/userimages/mn_images/image/CCs(1)%20png"
width="446">
This proves the said result
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PROVE THAT THE AREA OF THE SEMI CIRCLE DRAWN ON THE HYPOENUSE OF A RIGHT ANGLED TRIANGLE IS EQUAL TO THE SUM OF THE AREAS OF THE SEMICIRCLES DRAWN ON THE OTHER TWO SIDES OF THE TRIANGLE.