Question

The lines in the figure are tangent to the circle at points A and B. Find the measure of value of arcAB for m

Answer 1

110

Explanation:

There is a theorem that says "The measure of an angle formed by a secant and a tangent drawn from a point outside the circle is HALF the difference of the intercepted arcs "

Hence we can say:

`70=(1)/(2)(arcALB-arcAB)`

We can say:

`140=(arcALB-arcAB)`

Also, we know that circle's degree measure is 360, thus we can say:

`(arcALB+arcAB)=360`

To find Arc AB, we can use the two equations and add, thus we get:

`140=(arcALB-arcAB)\\360=(arcALB+arcAB)\\-------------\\500=2*arcALB\\arcALB=250`

Thus, arc AB = 360 - 250 = 110

2nd answer choice is right.