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2017 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 8

Revision as of 03:46, 19 January 2019 by Timneh (talk | contribs) (Created page with " == Problem == <asy> pair C=(0,0),A=(0,12),B=(5,0); draw(C--A--B--C,dot); MP("A",A,N);MP("C",C,SW);MP("B",B,E); real r=10/3; pair X=(0,r),Y=X+r*(12/13,5/13); draw(X--Y,dot...")
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Problem

[asy] pair C=(0,0),A=(0,12),B=(5,0); draw(C--A--B--C,dot); MP("A",A,N);MP("C",C,SW);MP("B",B,E); real r=10/3; pair X=(0,r),Y=X+r*(12/13,5/13); draw(X--Y,dot); MP("X",X,W);MP("Y",Y,NE); draw(circle(X,r)); MP("12",(0,8),W);MP("5",(2.5,0),S); [/asy]

Let $ABC$ be a right triangle with right angle at $C$. Suppose $AC = 12$ and $BC = 5$ and $CX$ is the diameter of a semicircle, where $X$ lies on $AC$ and the semicircle is tangent to side $AB$. Find the radius of the semicircle.

Solution

See also

2017 UNM-PNM Contest II (Problems • Answer Key • Resources)
Preceded by
Problem 7 		Followed by
Problem 9
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10
All UNM-PNM Problems and Solutions
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