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In circle O above, if ΔPOQ is a right triangle and radius OP is 2, wha

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In circle O above, if ΔPOQ is a right triangle and radius OP is 2, wha  [#permalink]

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New post 10 Jan 2019, 02:27
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

90% (01:14) correct 10% (01:00) wrong based on 15 sessions

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Location: India
Re: In circle O above, if ΔPOQ is a right triangle and radius OP is 2, wha  [#permalink]

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New post 10 Jan 2019, 03:03
In circle O above, if ΔPOQ is a right triangle and radius OP is 2, what is the area of the shaded region?

Given,
ΔPOQ is a right triangle
OP = radius = 2
implies OQ = 2 (as it is the radius)
Area of the Circle = \(Pi*r^2\)
= \(4*Pi\)

Area of the Triangle = \(1/2*base*height\)
= \(1/2*2*2\)
= 2

Area of the quarter circle = Area of the Circle/4 = Pi
implies area of the shaded region = Area of the quarter circle - area of the right triangle
= Pi - 2

Option E is correct
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Re: In circle O above, if ΔPOQ is a right triangle and radius OP is 2, wha  [#permalink]

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New post 10 Jan 2019, 05:48
Bunuel wrote:
Image
In circle O above, if ΔPOQ is a right triangle and radius OP is 2, what is the area of the shaded region?

A. 4π− 2
B. 4π− 4
C. 2π− 2
D. 2π− 4
E. π – 2


Attachment:
2019-01-10_1324.png



area of triangle opq = 0.5*2*2 = 2
opq is 1/4 of the circle ; 2*pi*2*.25 = pi
so shaded area = pi-2 IMO E
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Re: In circle O above, if ΔPOQ is a right triangle and radius OP is 2, wha   [#permalink] 10 Jan 2019, 05:48
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