SOLUTION: Question: AT and BT are tangents to a circle, center O and radius 10cm. The length of the arc AB is 16cm. find (a)the size of angle AOB. (b)the area of triangle ABT. an image of

Question 828031: Question: AT and BT are tangents to a circle, center O and radius 10cm. The length of the arc AB is 16cm. find (a)the size of angle AOB. (b)the area of triangle ABT.
an image of the diagram i sketched
http://postimg.org/image/eyky5f98h/
i solved (a) and it was 1.6 radians, however i couldn't find a way to calculate the area of triangle ABT as the shape OATB is a Kite and we only have the radius, angle AOB and angles TAO=TBO=pi/2
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
ABT is an isosceles triangle, with AT=BT.
You could calculate its area as
You need the measure of angle ATB, and the length of side AT.

Since you know 3 of the 4 angles in kite ATBO, you can easily calculate the measure of angle ATB, as
(rounded)

You can calculate AT from right triangle OAT.
Angle AOT is half of angle AOB, and
so

So the area of ABT is
(rounded).

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