Question

Given GH is tangent to ⊙T at N. If m∠ANG = 54°, what is mAB ? A circle with centre T is given. GH is tangent to the circle which touches the circumference of the circle at point N. From N, a diameter NTB is drawn. A chord AN is also given, this chord forms an acute angle with tangent. mAB = 72 °

Answer 1

Answer:

mAB=72°

Step-by-step explanation:

Theorem:The angle between a Tangent and a Radius is 90 degrees.

Applying the above theorem therefore:

∠ANG+∠ANB=90°

54°+∠ANB=90°

∠ANB=90°-54°

∠ANB=36°

Now, Inscribed Angle=$\frac{1}{2}$ of the measure of the arc

Therefore:

36°=$\frac{1}{2}X$ mAB

mAB=36*2=72°

Answer 2

The measure of arcAB is 72 degrees

Circle geometry

According to the theorem, the angle between a Tangent and a Radius is 90 degrees.

Applying the above theorem, therefore:

∠ANG+∠ANB=90°

54°+∠ANB=90°

∠ANB=90°-54°

∠ANB=36°

Since inscribed angle = of the measure of the arc

Therefore:

36°= mAB

mAB=36*2=72°

Hence the measure of arcAB is 72 degrees

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