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Question

# Consider the following statement: If a line segment joining two points subtends equal angles at two other points lying on the either side of the line, then all the four points will lie on a circle. The above statement is valid for which of the following cases?

A
Length of the said line segment is equal to radius of the circle.
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B
Length of the said line segment is half the radius of the circle.
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C
Length of the said line segment is twice the radius of the circle.
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D
The statement is incorrect.
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Solution

## The correct option is C Length of the said line segment is twice the radius of the circle.We know that if the line segment joining two points subtends equal angles at two other points lying on the same side of theline, then all the four points lie on a circle. However, the angle subtended by the diameter to any point on the circle is equal to 90o. Hence, the diamenter subtends equal angles at two other points lying on the same side or on opposite side of the diamenter. ∴ The required length of the line segment should be twice the radius of the circle to satisfy the given condition.

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