If AOB is a diameter of the circle and AC=BC, then `angle CAB` is equal to
A
`30^(@)`
B
`45^(@)`
C
`60^(@)`
D
`90^(@)`
Text Solution
Verified by Experts
The correct Answer is:
B
We know that, diameter subtends a right angle to the circle. `:. angleBCA=90^(@)...(i)` `"Given",AC=BC` `rArrangleABC=angleCAB ...(ii)` [angles opposite to equal sides are equal] In `DeltaABC, angleCAB+angleABC+angleBCA=180^(@)` [by angle sum property of a triangle] `rArr angleCAB+angleCAB+angle90^(@)=180^(@)["form Eqs. (i) and (ii)"]` `rArr 2angleCAB=180^(@)-90^(@)` `rArr angle CAB=(90^(@))/2` `:.angleCAB=45^(@)`
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