Circle Geometry

**Amanda92** · March 2nd 2009, 05:50 PM

23. Two circles intersect at A and B. The tangent to the first cirlce at A cuts the second circle at c and the tangent to the second circle at A cuts the first circle at D. Prove that Tri ABC and Tri DBA are similar.

Any Help appreciated

**red_dog** · March 3rd 2009, 06:32 AM

For the first circle:

$\left\{\begin{array}{ll}m(\widehat{DAB})=\frac{arc (AB)}{2}\\<br /> m(\widehat{ACB})=\frac{arc(AB)}{2}\end{array}\righ t.\Rightarrow \widehat{DAB}=\widehat{ACB}$

For the second circle:

$\left\{\begin{array}{ll}m(\widehat{BAC})=\frac{arc (AB)}{2}\\<br /> m(\widehat{ADB})=\frac{arc(AB)}{2}\end{array}\righ t.\Rightarrow \widehat{BAC}=\widehat{ADB}$

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