Circle geometry: Thales' theorem (angle in a semicircle is 90°) combined with the Pythagorean theorem. If AB² + BC² = AC², then angle ABC = 90°, meaning AC is a diameter.
Since AB=5, BC=12, AC=13, and 5²+12²=25+144=169=13², triangle ABC is right-angled at B, so AC (=13) is the diameter of the circle. Since AC is a...
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