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

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Math Expert
Joined: 02 Sep 2009
Posts: 55801
In circle O above, if ΔPOQ is a right triangle and radius OP is 2, wha  [#permalink]

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10 Jan 2019, 02:27
00:00

Difficulty:

25% (medium)

Question Stats:

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

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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 [ 14.59 KiB | Viewed 217 times ]

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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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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
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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10 Jan 2019, 05:48
Bunuel wrote:

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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