# Thread: Help with a geometry question

1. ## Help with a geometry question

I was wondering if anyone could

1)Check my interpretation/drawing of the question

2)Help me solve it

Here is the question:
A circle with centre P circumscribes triangle ABC (ie: touches each vertex). In the triangle: Angle A=75o and Angle B=60o. Construct tangents at points A and B, and extend them to intersect at D-outside the circle.

Show that ABD is an isosceles triangle with a right angle at D.

(Hint: you may need to construct some extra lines within triangle ABC)

Here is what I believe is described in the first paragraph:
IMG_0007.jpg picture by alexandersaver - Photobucket

Could anyone help me solve this( as well as where I would put the xtra lines)

Thanks

2. You don't have to construct extra lines.

$\displaystyle m(\widehat{DAB})=\frac{m(arcAB)}{2}=m(\widehat{C}) =45^{\circ}$

$\displaystyle m(\widehat{DBA})=\frac{m(arcAB)}{2}=m(\widehat{C}) =45^{\circ}$

So, $\displaystyle m(\widehat{DAB})=m(\widehat{DBA})=45^{\circ}\Right arrow m(\widehat{ADB})=90^{\circ}$