A point T is 17 cm from the centre of a circle of radius 8 cm…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A point T is cm from the centre of a circle of radius cm. Find the length of the tangent from T to the circle.
Need a reminder? The key ideaShow
The two tangents drawn from an outside point T to a circle are equal: . In the right triangle OPT, . The line OT bisects the angle and also the angle . In the figure OPTQ, . A tangent from an outside point has the same length on both sides of OT.
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 triangle. If the tangent touches the circle at P, then , cm and cm.
Step 2. Pythagoras. .
Step 3. The root. .
Answer: the tangent is cm long.
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