Question

What is the value of g?
The image is of a circle with a tangent and a secant, which are intersecting at an angle 38 degrees. Measure of smaller arc cut by them is g degrees and that of bigger arc is 119 degrees.

A. 124
B. 43
C. 100
D. 86

Answer 1

We have been given a circle with a tangent and a secant, which are intersecting at an angle 38 degrees. We are asked to find the measure of arc g.

We can see that angle with 38 degrees measure is a secant tangent angle outside the circle.

We know that measure of an angle formed by intersection tangent and secant outside circle is half the difference of intercepted arcs.

$38^{\circ}=\frac{1}{2}(119^{\circ}-g^{\circ})$

$38^{\circ}\cdot 2=\frac{1}{2}\cdot 2(119^{\circ}-g^{\circ})$

$76^{\circ}=119^{\circ}-g^{\circ}$

$76^{\circ}+g^{\circ}=119^{\circ}-g^{\circ}+g^{\circ}$

$76^{\circ}+g^{\circ}=119^{\circ}$

$76^{\circ}-76^{\circ}+g^{\circ}=119^{\circ}-76^{\circ}$

$g^{\circ}=43^{\circ}$

Therefore, the measure of smaller arc is 43 and option B is the correct choice.