## PROBLEM: Intersection of Lines through Points of Tangency |

Looking at the drawing below, prove that **A'C'** is congruent to
**C'B'**.

The solution put forth here is an algebraic means of solving the problem. The Law of Sines and Law of Cosines are used often in this solution.

Let, and .

Thus,

If **C'B' = A'C'**,

then.

Since, and, .

Therefore,

simplifies to .

Now defining each term in this last expression we get,

Thus,

becomes and after simplifying one is left with A'C' = C'B'.

Therefore, **A'C'** is congruent to **C'B'**.

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