Question

N the circle below, if arc AB = 124 °, and < BPA = 32 °, find the measure of arc CD.

Answer 1

Given:

where

`\begin{gathered} arcAB=124\degree \\ \angle BPA=32\degree \\ arcCD=x \end{gathered}`

To find the measure of arc CD, we use the secant-secant theorem.

According to the secant-secant theorem:

Thus, we have

`\begin{gathered} 32=(1)/(2)(124-x) \\ multiply\text{ both sides by 2} \\ \Rightarrow64=124-x \\ add\text{ -124 to both sides of the equation,} \\ -124+64=-124+124-x \\ -60=-x \\ \Rightarrow x=60 \end{gathered}`

Hence, we have the measure of arc CD to be

`60\degree`

The correct option is