Hello princesasabella

Welcome to Math Help Forum! Originally Posted by

**princesasabella** The problem says a chord length of 43 inches subtends a central angle of 157.8 degrees. There is a hint that says a line from the central angle is perpendicular to the chord, bisects both the angle and the chord. I have no clue how to figure this out. Thanks in advance.

Here's an alternative method that uses the hints you were given.

In the attached diagram, $\displaystyle M$ bisects $\displaystyle PQ$, $\displaystyle OM$ bisects $\displaystyle \angle POQ$, and $\displaystyle OM \perp PQ$. So we have:

$\displaystyle PM = 21.5$ in

$\displaystyle \angle POM = 78.9^o$

$\displaystyle \angle PMO = 90^o$

So in $\displaystyle \triangle POM$,

$\displaystyle \sin 78.9^o = \frac{21.5}{OP}$

Can you solve this equation to find $\displaystyle OP$, the radius of the circle?

Grandad