Show your proof.
The measure of a tangent-chord angle is half the measure of the intercepted arc inside the angle.
Can anyone prove this?
I've been trying to do it for the whole afternoon, help would be much appreciated, thanks.
=edit=
figured out the proof, trying to find a new one now.
Hello, lpbug!
Why don't you show us your proof?
Maybe we can find a different one?
The measure of a tangent-chord angle
is half the measure of the intercepted arc inside the angle.Code:* * * * * * * C * o * / * O * / * * o / * * | θ / * | / * | / * θ * | / * * |/ α * - - - - * o * - - - - B A
We have a circle with center
The chord is , the tangent is
Let
is a central angle, hence: .
is isosceles.
. . Hence: .
, so: .
. . Therefore: . . . . . Q.E.D.