SOLUTION: The chord AB of a circle whose centre is O is 10cm long and AOB = 140 degre. Calculate the radius of the circle

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Question 1132230: The chord AB of a circle whose centre is O is 10cm long and AOB = 140 degre. Calculate the radius of the circle
Answer by MathLover1(20850) About Me  (Show Source):
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The chord AB of a circle whose centre is O is 10cm long and < AOB+=+140°. Calculate the radius of the circle

If you draw the diagram with radii you will realize you have an isosceles triangle whose base length and angles you know.


Thus you can divide it into two congruent right triangles and calculate the radius using sine.
if
AB=10cm+

< AOB+=+140° => and AOB is an isosceles triangle
and midpoint of AB is M divide AOB into two congruent right triangles: AOM and MOB
since AO=r and OB=r and < AOB+=+140° is divided into two angles, each measure 70°
then
sin%2870%29=AM%2Fr
The radius r is the hypotenuse of a right-angled triangle and distance from center OM and half the length of the chord.
AM=5cm
sin%2870%29=5%2Fr
r=5%2Fsin%2870%29
r=5.3cm