Problem
Given circle \( E \) with diameter \( \overline{C D} \) and radius \( \overline{E A} \cdot \overline{A B} \) is tangent to \( E \) at \( A \). If \( A C=28 \) and \( E A=17 \), solve for \( E C \). Round your answer to the nearest tenth if necessary. If the answer cannot be determined, click "Cannot be determined." Answer: Submit Answer
Solution
Step 1 ：\(\triangle AEC \) is a right triangle, as \(AC \) is tangent to circle \(E\) at \(A\).
Step 2 ：Apply Pythagorean theorem: \(AC^2 = AE^2 + EC^2\)
Step 3 ：Solve for \(EC\): \(EC = \sqrt{AC^2 - AE^2}\)
Step 4 ：Calculate \(EC\): \(EC = \sqrt{28^2 - 17^2} \approx 21.5\)
