Question

65 Points - I have class in 1hr and I still can't figure this out... pls give full explanation and correct answer or else you'll be reported for "point greediness" --- thx ya'll

AB is tangent to the circle k(O) at B, and ADis a secant, which goes through O. Point O is between A and D∈k(O). Find m∠BAD and m∠ADB, if measure of arc BD is 110°20'.

Answer 1

Sounds like the situation in the sketch below...

There is a theorem that says the angle (BAD) formed by a tangent (AB) and a secant (AD) to a circle (O) is half the difference of the intercepted arcs (BD and BD'):

`m\angle BAD=\frac{110^\circ20'-69^\circ40'}2=40^\circ40'`

Triangle BAD is a right triangle, so

`m\angle ADB=90^\circ-m\angle BAD=49^\circ20'`