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# In the circle above, chords AC and BD intersect at point P. If PD/PC

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Re: In the circle above, chords AC and BD intersect at point P. If PD/PC [#permalink]
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Bunuel wrote:

In the circle above, chords AC and BD intersect at point P. If PD/PC = 5/3, what is the length BP?

(1) AP=10
(2) Angle BPC measures 90 degrees.

Attachment:
IntersectP.png

PAB and PCD will be similar triangles and we have the ratio of sides in one the triangles that would be same for the second triangles as well so we need only AP to find out BP

Statement 1: SUFFICIENT
Statement 2: NOT SUFFICIENT

Answer: option A
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Re: In the circle above, chords AC and BD intersect at point P. If PD/PC [#permalink]
GMATinsight wrote:
Bunuel wrote:

In the circle above, chords AC and BD intersect at point P. If PD/PC = 5/3, what is the length BP?

(1) AP=10
(2) Angle BPC measures 90 degrees.

Attachment:
IntersectP.png

PAB and PCD will be similar triangles and we have the ratio of sides in one the triangles that would be same for the second triangles as well so we need only AP to find out BP

Statement 1: SUFFICIENT
Statement 2: NOT SUFFICIENT

Answer: option A

Halo GMATinsight, how can we conclude that PAB and PCD will be similar? There is no information about the other two angles in each triangle.
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Re: In the circle above, chords AC and BD intersect at point P. If PD/PC [#permalink]
AHH!! I forgot about the concept about same angles which hold the same chord!

Thanks for reminding GMATinsight !
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In the circle above, chords AC and BD intersect at point P. If PD/PC [#permalink]
Reviewing the question, triangles ABP and PCD are similar because of the following:
1) Angle APB = angle CPD (vertically opposite angles are equal)
2) Angle ABP = angle PCD (angles formed by chord AD at the circumference are equal)
3) Angle PAB = angle PDC (angles formed by chord BC at the circumference are equal)

We are also given: PD/PC = 5/3

Statement 1: AP =10

Since triangles ABP and PCD are similar, PD / AP = PC / BP. Using AP = 10 and PD/PC = 5/3, we can solve for BP.
Hence, statement 1 is sufficient

Statement 2: Angle BPC measures 90 degrees

This statement does't provide any information on the other sides or angles of the triangles. Hence, insufficient.
In the circle above, chords AC and BD intersect at point P. If PD/PC [#permalink]
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