Math Problem Statement

In triangle $ABC,$ $\angle C = 90^\circ.$ A semicircle is constructed along side $\overline{AC}$ that is tangent to $\overline{BC}$ and $\overline{AB}.$ If the radius of the semicircle is equal to $\frac{BC}{4},$ then find $\frac{AC}{BC}.$

Solution

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Math Problem Analysis

Mathematical Concepts

Geometry
Right Triangle
Circle Tangency

Formulas

Pythagorean theorem

Theorems

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Suitable Grade Level

High School