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# Circles P and Q each have a circumference of 10π and are eac

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Circles P and Q each have a circumference of 10π and are eac [#permalink]  31 Jul 2020, 10:12
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59% (02:31) correct 40% (02:37) wrong based on 22 sessions
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Circles P and Q each have a circumference of $$10\pi$$ and are each tangent to YZ.   If   XZ = 17, then YZ =

A. 10

B. 85/6

C. 43/3

D. 15

E. 17
[Reveal] Spoiler: OA

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Re: Circles P and Q each have a circumference of 10π and are eac [#permalink]  02 Aug 2020, 02:40
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PQ= 10 ,XZ=17
QZ=5, XQ=12
Using congruency rule
PQ/YZ=XQ/XZ
YZ=(17 x 10)/12
YZ=85/6

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Re: Circles P and Q each have a circumference of 10π and are eac [#permalink]  02 Aug 2020, 04:28
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Re: Circles P and Q each have a circumference of 10π and are eac [#permalink]  03 Aug 2020, 02:32
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Re: Circles P and Q each have a circumference of 10π and are eac [#permalink]  06 Oct 2020, 01:49
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Answer is b) 85/6

2*pi*r = 10*pi => r = 5

Then, PQ = 2r = 10
QZ = r = 5
XQ = XZ - QZ = 17 - 5 =12

Since

Now, consider triangles XYZ and XPQ

The line YZ is perpendicular to the radius at the point of intersection.

Hence, PQ is parallel to YZ

This means that angle P = angle Y and angle Q = angle Z

We also have angle X is common,

This means that XYZ AND ZPQ are similar

=> YZ/XZ = PQ/XQ

=> YZ/17 = 10/12

=> YZ = 5/6 * 17

=> YZ = 85/6
Re: Circles P and Q each have a circumference of 10π and are eac   [#permalink] 06 Oct 2020, 01:49
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# Circles P and Q each have a circumference of 10π and are eac

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