Circle Tangent Chord Problem

This is another problem from the Math Challenges section of the 2000 Pi in the Sky Canadian math magazine for high school students.

Problem 4. From a point P on the circumference of a circle, a distance PT of 10 meters is laid out along the tangent. The shortest distance from T to the circle is 5 meters. A straight line is drawn through T cutting the circle at X and Y. The length of TX is 15/2 meters.

(a) Determine the radius of the circle,
(b) Determine the length of XY.”

See the Circle Tangent Chord Problem

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