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Question
In the following figure, if AOB is a diameter of the circle and AC = BC, then ∠CAB is equal to ______.
Options
30º
60º
90º
45º
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Solution
In the following figure, if AOB is a diameter of the circle and AC = BC, then ∠CAB is equal to 45º.
Explanation:
We know that, diameter subtends a right angle to the circle.
∴ ∠BCA = 90º ...(i)
Given, AC = BC
⇒ ∠ABC = ∠CAB ...(ii) [Angles opposite to equal sides are equal]
In ΔABC, ∠CAB + ∠ABC + ∠BCA = 180º ...[By angle sum property of a triangle]
⇒ ∠CAB + ∠CAB + ∠90º = 180º ...[From equations (i) and (ii)]
⇒ 2∠CAB = 180º – 90º
⇒ ∠CAB = `(90^circ)/2`
∴ ∠CAB = 45º
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