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# In the figure above, circle P and circle R, with centers P and R respe

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Math Expert
Joined: 02 Sep 2009
Posts: 50711
In the figure above, circle P and circle R, with centers P and R respe  [#permalink]

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28 Nov 2017, 20:01
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Difficulty:

(N/A)

Question Stats:

78% (01:35) correct 22% (01:46) wrong based on 14 sessions

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In the figure above, circle P and circle R, with centers P and R respectively, intersect at Q and S. If circle P is larger than circle R, which of the following must be true?

I. Area of ∆ PQR = Area of ∆ RSP
II. Area of ∆ PSQ = area of ∆ QRS
III. PR and QS bisect each other

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III

Attachment:

2017-11-28_1024_002.png [ 10.61 KiB | Viewed 386 times ]

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Re: In the figure above, circle P and circle R, with centers P and R respe  [#permalink]

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28 Nov 2017, 20:37
A

I. Triangle PQR and PRS lie on the same base and also PQ=PS, QR=RS. Hence their areas are equal
II. Triangle PQS and QRS lie on the same base however PQ is not equal to QR and PS is not equal to RS. Hence their areas are not equal. But they are isosceles triangle with proportionate areas.
III. QS is bisected always as PR lies at the mid point. However PR is not bisected always as it depends on the distance between P and R

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Re: In the figure above, circle P and circle R, with centers P and R respe &nbs [#permalink] 28 Nov 2017, 20:37
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