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21 Mar 2022, 05:45
Kudos
Bookmarks
B
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Difficulty:
55%
(hard)
Question Stats:
62% (03:08) correct
38%
(03:13)
wrong
based on 66
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Circles P and Q each have a circumference of 10π and are each tangent to YZ. If XZ = 17, then YZ =
A. 10
B. 85/6
C. 43/3
D. 15
E. 17
Are You Up For the Challenge: 700 Level Questions
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Bunuel
Finding radius,
Therefore, radius= 5.
Now throwing a perpendicular from point P to the side YZ and naming the new point as point L.
PL=5(radius)
Now, Triangle YPL is similar to Triangle YXZ.
Using SIDE : AREA similarity relationship,
\(\frac{PL}{XZ}\) = \(\frac{YL}{YZ}\)
We can write YL= YZ-10( Radius of two circles).
\(\frac{PL}{XZ}\) = \(\frac{YZ-10}{YZ}\)
PL=5(radius of circle with point P) , XZ =17(given)
\(\frac{5}{17}\) = \(\frac{YZ-10}{YZ}\)
Solving, we get
5YZ = 17YZ - 170,
12YZ = 170,
YZ= \(\frac{85}{6} \)
Methinks its B.
Do correct me if i am wrong.
22 Mar 2022, 07:14
Kudos
Bookmarks
Hi,
we can calculate the radius form the circumference:
10*pi=2*pi*r
-> r=5
-> XQ=12
For the triangle QPZ, we see that QP=10.
QPZ is similar to XZY -> YZ/10=17/12 -> YZ=170/12=85/6 ->B
we can calculate the radius form the circumference:
10*pi=2*pi*r
-> r=5
-> XQ=12
For the triangle QPZ, we see that QP=10.
QPZ is similar to XZY -> YZ/10=17/12 -> YZ=170/12=85/6 ->B
