Question

3. In the diagram of circle 0, two tangents have been drawn from exterior point P to the circle at points A and B. (a) If mAB =105 , then determine the measure of ZP. Show your work.

Answer 1

75

Explanation:

Given:

mAB =105

The minor arc given mAB is 105. Subtract that from 360 to get the measure of the major arc mACB

<=> mACB = 360 - 105 = 255

As we know, the measure of an angle formed by two tangents intersesting outside the circle can be found by one haft of the difference between the mearsure of two intercepted arcs

=> the measure of ∠P is:

= (mACB - mAB)/ 2

= (255 - 105)/2

= 75