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
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
For the first circle:
$\displaystyle \left\{\begin{array}{ll}m(\widehat{DAB})=\frac{arc (AB)}{2}\\
m(\widehat{ACB})=\frac{arc(AB)}{2}\end{array}\righ t.\Rightarrow \widehat{DAB}=\widehat{ACB}$
For the second circle:
$\displaystyle \left\{\begin{array}{ll}m(\widehat{BAC})=\frac{arc (AB)}{2}\\
m(\widehat{ADB})=\frac{arc(AB)}{2}\end{array}\righ t.\Rightarrow \widehat{BAC}=\widehat{ADB}$