PT is a tangent to a circle with centre O, touching it at P…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
PT is a tangent to a circle with centre O, touching it at P. The line OT meets the circle at A. . Find .
Need a reminder? The key ideaShow
A tangent meets a circle at exactly one point, and the tangent at P is perpendicular to the radius OP. A line at distance from the centre meets a circle of radius at two points if , at one point if , and at none if . In the right triangle OPT, with the right angle at P, . The angles of a triangle add up to .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The right angle. The radius OP is perpendicular to the tangent PT, so .
Step 2. The angle sum. In , .
Step 3. Subtract. .
Answer: .
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