Math CentralQuandaries & Queries


Question from Doug, a student:

Two distinct, nonparallel lines are tangent to a circle. The measurement of the angle between the two lines is 54 degrees (angle QVP).
Suppose the diameter of the circle is 2 cm. What is the distance VP? Suppose the distance VP is 3.93 cm. What is the diameter of the circle? Find a formula for d, the diameter of the circle, in terms of VP.
Find a formula for VP in terms of d, the diameter of the circle.

Hi Doug.

Remember that a line that is tangent to a circle is perpendicular to its radius at the point of tangency. That means that when you draw this, you get right-angled triangles. That let's you solve the problem using simple trig functions like sine, cosine and tangent and use the Pythagorean Theorem as well. Try drawing it and you will see at once what I mean.

Stephen La Rocque.>

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