Question

True or False. The measure of a tangent-chord angle inside is half the measure of the intercepted arc outside the angle

Answer 1

true

Explanation:

Answer 2

1. TRUE

2. Check the picture.

3. let l be a line tangent to the circle with center O, at point A.

4. Let T be another point on the tangent line l, as shown in the picture.

m(OAT)=90°, as the angle formed by the radius and the tangent

5. Let m(AOB)=α, m(OAB)=m(OBA)=β, as OA=OB, both radii


6. In triangle AOB:
α+β+β=180°
α+2β=180°, divide by 2:

α/2+β=90°

90°-β=α/2


7. The arc AB is also intercepted by the central angle AOB, with measure α, so its measure is half of α.


8. the measure of the angle formed by the tangent and the chord angle is half of the measure of the intercepted arc.