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 =
`(1)/(2) * arc(ADC)`

∠4 =
`(1)/(2) * arc(AC)`

∠2 = ∠3 - ∠4

∠2 =
`(1)/(2) * arc(ADC)` -
`(1)/(2) * arc(AC)`

∠2 =
`(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.