A circle has radius 6.5 cm. Three straight lines are drawn at distances 4 cm, 6.5 cm and 8 cm from…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A circle has radius cm. Three straight lines are drawn at distances cm, cm and cm from the centre. How many points does each line share with the circle?
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 line at cm. , so the line cuts the circle. It is a secant with common points.
Step 2. The line at cm. , so the line touches the circle. It is a tangent with common point.
Step 3. The line at cm. , so the line is outside the circle. It has common points.
Answer: , and .
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