Question

The diagram shows three circles externally tangent to each other and to a semicircle.The shaded area is 120 sq.units. The area of the unshaded parts of the semi circle in square units is

• A. 30
• B. 80
• C. 40
• D. 60

Answer 1

Answer: (B), (C)

The correct options are
B

80

C

40

Let the radius of the semi circle on AB be 2r units.Let the radii of the circles with conters P and Q

Be x units and y units respectively. Draw PK perpendicular to QO.
The radius of the circle with centre Q is r units.Now,
PQ=(r+x) units,

QK= (r-x) units and

OP=OL-PL=(2r-x) units.
From right angled ∆PQK, PQ²-QK²=PK²= OP²-OK²
i.e., (r+x)² - (r-x)² = PK² = (2r-x)²-x²
or4rx = 4r² - 4rx
or8rx= 4r²

Hence r=2x