Question

GEOMETRY HELP? Circle O is shown below. What is the measure of BAC?

(even if you just have the formula that would be helpful)
A.53.5
B.146
C.36.5
D.107

Answer 1

A.
`53.5^(\circ)`

Explanation:

We have been given an image of a circle. We are asked to find the measure of angle BAC.

We can see that angle BAC and central angle BOC corresponds to same arc BC. By inscribed angle theorem measure of angle BAC would be half the measure of central angle BOC.

We can see that AC is diameter of circle as it passes through the center of our given circle. We will use linear pair of angles to find the measure of central angle BOC as:

`m\angle BOA+m\angle BOC=180^(\circ)`

`73^(\circ)+m\angle BOC=180^(\circ)`

`73^(\circ)-73^(\circ)+m\angle BOC=180^(\circ)-73^(\circ)`

`m\angle BOC=107^(\circ)`

Since BAC is inscribed angle, so its measure would be half the measure of central angle BOC.

`m\angle BAC=(107^(\circ))/(2)`

`m\angle BAC=53.5^(\circ)`

Therefore, the measure of angle BAC is 53.5 degrees and option A is the correct choice.