Answer :
We have to use the following theorem
An Angle formed by a chord and a tangent that intersect on a circle is half the measure of the intercepted arc .
And it is given that arc m BC = 89 degree.
[tex] \angle BCP = \frac{1}{2}( m BC) [/tex]
[tex] \angle BCP = \frac{1}{2}( 89)=44.5 [/tex]
Correct option is A.
Final answer:
Angle mBCP measurement is found by adding the 90-degree angle BCP, as PQ is a tangent, with half of the arc mBC measurement (44.5 degrees). The answer is 134.5 degrees, which doesn't match any of the given options, indicating an error in the choices.
Explanation:
The question asks for the measurement of angle mBCP in a circle where PQ is a tangent at point C, and the arc mBC measures 89 degrees. Since PQ is a tangent, and C is the point of tangency, angle BCP would be a right angle (90 degrees) because a tangent to a circle forms a 90-degree angle with the radius at the point of tangency.
However, the other part of angle mBCP is half of the arc mBC (by the Inscribed Angle Theorem), which is 89 degrees. Therefore, half of 89 degrees is 44.5 degrees. We then add this to the 90 degrees of the right angle to find the measure of angle mBCP.
The measure of angle mBCP is 90 + 44.5 = 134.5 degrees. Unfortunately, this measurement is not among the provided options A (44.5), B (89), C (91), or D (178), suggesting a typo or error in the options given.
