A chord lenght 12 cm subtends an angle of 78.2 at the center of a circle. find the radius of the circle
Answers
Explanation 1
If you draw a triangle inside the circle with the base being 12 cm long and the top angle being 78.2 degrees, this is an isosceles triangle with each side equal to the radius of the circle.
You can drop a perpendicular to the base. This new line bisects the angle and bisects the base so now you have a right triangle with the angle equal to 39.1 degrees and the opposite side equal to 6 cm. The hypotenuse is the radius.
So find the sine of 39.1 degrees which equals opposite / hypotenuse = 6 / radius
Explanation 2
Draw and label of diagram thus:
O is the center of the circle
A and B are the endpoints of the chord
Draw perpendicular bisector from center to chord.
C is the intersection of perpendicular and chord.
∠COB = 39.1°
∠CBO = 50.9°
Use either
cos 50.9° = 6/r or
sin 39.1°= 6/r
to solve for the radius.