For a given circle with a center O and radius OA, if two arcs B and C are drawn on the circumference of the circle from 1 by taking the measurement of OA as the radius of the arc, what will be the shape of the triangle obtained by joining the points 1, B and C?
Answers
Answer:
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The shape of the triangle obtained by joining points 1, B, and C is a right-angled triangle.
Given:
For the circle,
Centre = O
radius = OA
To find:
We need to find the shape of the triangle that is obtained by joining points 1, B, and C.
Solution:
As we know that the angle subtended by an arc at the center is double the angle subtended at any other point or the circumference.
Therefore, the angle subtended by arc AB at O = Double the angle subtended at C.
=> ∠AOB = 2∠ACB
AOB is a straight line.
∠AOB = 180°
=> 2∠ACB= 180°
=> ∠ACB= 90°
Therefore the angle subtended by AB is 90°.
Hence, it is a right-angled triangle.
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