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

• Jan 20th 2010, 04:02 PM
princesasabella
Help with finding the radius of a circle....
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.
• Jan 20th 2010, 04:21 PM
skeeter
Quote:

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 $r$
• Jan 21st 2010, 02:58 AM
Hello princesasabella

Welcome to Math Help Forum!
Quote:

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:
$PM = 21.5$ in

$\angle POM = 78.9^o$

$\angle PMO = 90^o$
So in $\triangle POM$,
$\sin 78.9^o = \frac{21.5}{OP}$
Can you solve this equation to find $OP$, the radius of the circle?