Question

1. Given the information in the diagram of circle P at right, calculate: (6 points)a. mBCb. m ZAc.MAB.

Answer 1

a. mBC = 45°

b. mc. mAB = 157.5°

Explanation:

a.

The value of the arc BC is equal to the angle P, that is, 45 °, since if the point is in the center of the circle, the value of the angle is equal to the value of the arc.

b.

The value of the angle of A is equal to the half of the arc that is formed, therefore

`\begin{gathered} A=(1)/(2)BC \\ A=(1)/(2)\cdot45\text{\degree} \\ A=22.5\text{\degree} \end{gathered}`

c.

We know that the arcs AB and AC are equal and that the sum of the three arcs is equal to 360 °, which is what a circle measures in its entirety.

Therefore we can propose the following equation:

`\begin{gathered} 360=AB+AC+BC \\ AB=AC \\ 360=2AB+45 \\ 2AB=360-45 \\ AB=(315)/(2) \\ AB=157.5 \end{gathered}`