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# In the figure, ABCD is a square, and OB is a radius of the circle. If

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
In the figure, ABCD is a square, and OB is a radius of the circle. If  [#permalink]

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15 Oct 2018, 07:02
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00:00

Difficulty:

25% (medium)

Question Stats:

85% (01:06) correct 15% (01:15) wrong based on 44 sessions

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In the figure, ABCD is a square, and OB is a radius of the circle. If BC is a tangent to the circle and PC = 2, then what is the area of the square?

(A) 16

(B) 20

(C) 25

(D) 36

(E) 42

Attachment:

figure.jpg [ 21.14 KiB | Viewed 427 times ]

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Re: In the figure, ABCD is a square, and OB is a radius of the circle. If  [#permalink]

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15 Oct 2018, 07:26
1
Bunuel wrote:

In the figure, ABCD is a square, and OB is a radius of the circle. If BC is a tangent to the circle and PC = 2, then what is the area of the square?

(A) 16

(B) 20

(C) 25

(D) 36

(E) 42

Given, BC is a tangent to the circle. Hence, Angle OBC=90 degree Or, OBC is a right angled triangle with OB=3 and OC=OP+PC=3+2=5.
Therefore, BC=third side of triangle=Side of square=$$\sqrt{5^2-3^2}$$=4

Hence, area of the square=$$4^2=16$$
Ans. (A)
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Joined: 26 Jun 2018
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Re: In the figure, ABCD is a square, and OB is a radius of the circle. If  [#permalink]

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15 Oct 2018, 14:40
Triangle OBC is a right triangle with shortest side 3, making it a 3,4,5 right triangle. Thus the side of the square is 4 and the area is 16.
Re: In the figure, ABCD is a square, and OB is a radius of the circle. If   [#permalink] 15 Oct 2018, 14:40
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