## Outline Mathematics

Geometry

# Two Touching Circles

Consider the following problem:

Two circles with centers P and Q touch at point A. A line through A meets the first circle again at B and the second at C. Show that

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Copyright © 1996-2018 Alexander Bogomolny
Two circles with centers P and Q touch at point A. A line through A meets the first circle again at B and the second at C. Show that

Angles BAP and CAQ are vertical,vertical,alternate,exterior and hence equal. Triangles BAP and CAQ are isosceles,right,equal,isosceles with equal base angles at A. The other pair of the base,alternate,base angles are also equal. I.e.,

(The terms you met: Vertical angles, Alternate angles, Transversal, Isosceles triangle)

### References

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