# Circle geometry

• Mar 7th 2009, 12:34 PM
Amanda92
Circle geometry
21. Two points A and b are taken on a circle and C in the other end of the diameter through A. If AE is the perpendicular from A ont ot he tangent at B, prove that AB bisects angle CAE.
• Mar 7th 2009, 12:54 PM
red_dog
$m(\widehat{BAC})=\frac{m(arcBC)}{2}$

$m(\widehat{EBA})=\frac{m(arcAB)}{2}$

$m(\widehat{EAB})=90^{\circ}-m(\widehat{EBA})=90^{\circ}-\frac{m(arcAB)}{2}=\frac{180^{\circ}-m(arcAB)}{2}=\frac{m(arcBC)}{2}$

Then $m(\widehat{BAC})=m(\widehat{EAB})$