A circle has a circumference of 450cm An arch of the circle has length of 90cm angle
Find the angle which this arc subtends at the center of the circle

The circumference of the circle is actually the perimeter ( length of the boundary ) of the circle . And a part of the circle which lies between two distinct points on the circumference of the circle is called an arc . If the length of the arc is less than half the circumference , it is called minor arc and remaining portion which is more than half of the circle ( but natural ) is called major arc .

When these two points , which make the arc are joined separately to the centre of circle , these arms make angle at the centre . This is called the angle subtended by the arc at the centre of the circle .

There is a beautiful logical relation exists between arc length and the angle , the arc makes ( subtends ) at the centre of the circle . This relation is as under , the wholle circle subtends an angle of 360 degree at the centre . Half the circumference subtendr 360 / 2 ie 180 degree at the centre . The logical relation becomes Arc Length = Circumference × angle in degrees it ( the arc ) subtends at the centre of the circle / 360 degree . So the answer is very simple :- The Arc Length = 36 × 90 / 360 or 9 units ( may be centimetres or metres or inches , feet , yards , etc ) . Which is definitely length of the minor arc . The length of the major arc ( remaining portion of the circumstance ) is 36 - 9 = 27 units . Hence the required answer of the sum is 9 units .

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