In the figure, two circles touching each other, and a semicircle is made on diameter AB, PQ is the tangent which touches both the circle, then find the area of the shaded portion.?

9π cm²
7π cm²
11π cm²
8π cm²

LohaHridoy

5 views

2025-01-04 04:42

1 Answers

AhmedNazir

Option 1 : 9π cm2

Let the radius of the bigger circle be R cm and radius of the smaller circle be r cm.

⇒ PQ = 2√(Rr)

⇒ 6 = 2√(Rr)

⇒ Rr = 9 cm

The radius of the semicircle made on diameter AB = R + r

⇒ Area of shaded portion = π/2(R + r)² – Area of the semicircle of radius R – Area of the circle of radius r

⇒ Area of shaded portion = π/2(R + r)² – π/2 × R² – π/2 × r²

⇒ Area of shaded portion = π/2

⇒ Area of shaded portion = π/2 × 2Rr

∴ Area of shaded portion = 9π cm²

5 views Answered 2022-09-04 04:29

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