Question
Segments OA and OB are radii of the semicircle above. Arc AB has length 3π and OA = 5. What is the value of x ?
Hint:
Hint:
We are given the radius of the circle and an arc length. We need to find the angle subtended by the arc on the centre O.
The formula to be used is
where, = arc length (in radians); r = radius; 
=angle (in radians)
If is in degree, we use the formula
We need to input the given values of s and r in the above formula and find the value of .
The correct answer is: 108
Let s denote the length of the arc AB
Let r denote the radius OA of the circle.
Let denote the angle subtended by the arc AB on the centre,
Given,
To find: the value of x in degrees
We know,
To calculate the value of x , we keep x on one side of the equation and take all the other quantities on the other side,
Now, we use the given values in the above equation
By simplifying, we get
Thus, the angle subtended at the centre is given by 
The correct answer is 108.
A semicircle is formed when a lining passing through the center touches the circle's two ends. As a result of joining two semicircles, we get a circular shape.
A circle is a collection of points equidistant from the circle's center. A radius is a common distance between the center of a circle and its point.
¶Area of a semicircle = 1/2 (π r2)
where r is the radius.
The value is 3.14 or 22/7.
¶Semi circle Formula
¶
| Area | ¶(πr2)/2 | ¶
| Perimeter (Circumference) | ¶(½)πd + d; when diameter (d) is known πr + 2r | ¶
| Angle in a semicircle | ¶¶90 degrees, i.e., right angle ¶ | ¶
| Central angle | ¶180 degrees | ¶
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