ABC is a right angled triangle right angled at B.semi circles is drawn on AB, BC, CA as daimeter. show that the sum of areas of semicircles dr on AB and BC as daimeter is equal to the area of semicircle drawn on CA as daimeter. plz tell
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Answer:
plss figure it out.
Step-by-step explanation:
rea of shaded region = area of semicircle AB + area of semi-circle AC - (area of semicircle on side BC) + area of ΔABC
Area of semicircle AB = πr
2
=
7
22
×
2
3
×
2
3
=7.07 sq. units
Area of semicircle AC = πr
2
=
7
22
×2×2=12.57 sq. units
Area of semicircle BC = πr
2
=π×(
2
BC
)
2
Now, BC=
4
2
+3
2
=
25
=5
∴ Area of semi-circle BC =
7
22
×(
2
5
)
2
=19.64 sq. units.
Area ΔABC=
2
1
×AB×AC=
2
1
×3×4=6 sq. units
Therefore, area of shaded region= 7.07+12.57−19.64+6
= 6 sq. units
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ABC is a right angle triangle
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