Question

The lines in the figure are tangent to the circle at points A and B. Find the measure of value of arc AB for angle P=36. (The figure is not drawn to scale.)

A. 288
B. 18
C. 144
D. 72

Answer 1

The measure of the value of arc ab for angle p is 18

Answer 2

Option C.

Explanation:

Given information: Line PA and PB tangent to the circle,
`\angle P=36^(\circ)`.

Draw the radius from the point A and B.

The tangent to a circle is perpendicular to the radius at the point of tangency.

`\angle PAO=\angle PBO=90^(\circ)`

OAPB is a quadrilateral and the sum of all interior angles of a quadrilateral is 360°.

`\angle AOB+\angle PAO+\angel APB+\angle PBO=360`

`\angle AOB+90+36+90=360`

`\angle AOB+216=360`

Subtract 216 from both sides.

`\angle AOB=360-216`

`\angle AOB=144`

The measure of arc AB is 144°.

Therefore, the correct option is C.