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| Math Central | Quandaries & Queries |
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Question from Aishwarya, a student: The angles of a triangle are 50, 60, and 70 degrees, and a circle is touches the sides at A, B, C. Calculate the angles of the triangle ABC. Not understanding how to draw the diagram...Please help.... |
Hi,
Her is my diagram. (The angle measurements are incorrect.)
There are three facts that will help you with this problem.
- A tangent line to a circle and the radius that intersects the circle at the point of tangency are perpendicular. For example $PB$ and $BQ$ are perpendicular.
- The sum of the angles in a triangle is $180^o$.
- The angle subtended by a chord at the circumference of a circle is half the angle subtended at the center.
Penny
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