Common tangent of two intersecting circles and the area of the region inside at least one of them
Common tangent of two intersecting circles and the area of the region inside at least one of them
IB Year 6 | Grade 12
10 marks
Two circles intersect. One has centre \(P\) and radius \(3\), and the other has centre \(Q\) and radius \(7\), where \(PQ=8\). A common tangent touches the first circle at \(S\) and the second circle at \(T\), as shown in the diagram below.
- Find the exact length of \(ST\).[2]
- Find \(\angle PQT\).[2]
- Find the area of the region that lies inside at least one of the two circles.[6]
Solution:
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Answer:(a) \(ST=4\sqrt3\) (b) \(\angle PQT=\frac{\pi}{3}\ (60^\circ)\) (c) \(175\) square units
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