Track / Stage 4 / 45 of 340 #305 of 1964

Problem 305

AMC 12 late, AIME early

Geometry Difficulty 4.6 Find the answer

4. (7 points) Point $B$ lies on segment $A C$ , with $A B=14, B C=28$ . On segments $A B, B C, A C$ as diameters, semicircles are constructed in the same half-plane. Find the radius of the circle that is tangent to all three semicircles.

The source for this one didn't record the answer, so there is nothing to check what you type against. Work it on paper and mark yourself against the solution below.

Official solution

# Solution.

segments $A B, B C, A C$ .

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.