Help with finding the radius of a circle....

**princesasabella** · January 20th 2010, 04:02 PM

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.

**skeeter** · January 20th 2010, 04:21 PM

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.

the chord and the two radii that intersect the chord's endpoints form a isosceles triangle with side lengths $r$ , $r$ , and 43.

law of cosines ...

$43^2 = r^2 + r^2 - 2r^2 \cos(157.8)$

solve for $r$

**Grandad** · January 21st 2010, 02:58 AM

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, $M$ bisects $PQ$ , $OM$ bisects $\angle POQ$ , and $OM \perp PQ$ . So we have: