Math CentralQuandaries & Queries


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....
The ans is 55 60 and 65...Don't know how to get it


Her is my diagram. (The angle measurements are incorrect.)


There are three facts that will help you with this problem.

  1. 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.

  2. The sum of the angles in a triangle is $180^o$.

  3. The angle subtended by a chord at the circumference of a circle is half the angle subtended at the center.


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