Question

True or False!!!! The measure of a tangent-tangent angle is twice the difference of the measures of the intercepted arcs.

Answer 1

answer : False

The measure of a tangent-tangent angle is one - half the difference of the measures of the intercepted arcs.

The diagram is attached below

AB  and BC are the two tangents

By exterior angle theorem

 ∠3 = ∠2 + ∠4

So   ∠2 = ∠3 - ∠4

Now we find angle 3  and 4, we know when a chord and tangent intersect at a point then the measure of angle is one half of measure of intercepted arc

∠3 = $\frac{1}{2} * arc(ADC)$

∠4 = $\frac{1}{2} * arc(AC)$

 ∠2 = ∠3 - ∠4

 ∠2 = $\frac{1}{2} * arc(ADC)$  -  $\frac{1}{2} * arc(AC)$

∠2 = $\frac{1}{2} ( arc(ADC) - arc(AC))$

The measure of a tangent-tangent angle is one half the difference of the measures of the intercepted arcs.