Question

AOB is diameter. AC=BC then angle CAB is equal to

Answer 1

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Answer 2

The value of $\angle$CAB = 45°.

Step-by-step explanation:

We are given in the figure that AOB is diameter and sides AC = BC.

In the figure, as we know that the angle subtended at the circumference of the circle by the diameter of the circle is of right angle, that means;

$\angle$ACB = 90°        {right angle}

Since the sides AC and BC are equal, this means that;

$\angle$CAB = $\angle$CBA --- (1)  {because the equal sides have equal opposite angles}

Now, considering the triangle ABC;

$\angle$ACB + $\angle$CAB + $\angle$CBA = 180°   {angle sum property of the triangle}

90° + $\angle$CAB + $\angle$CAB = 180°     {using condition 1}

90° + 2$\angle$CAB = 180°

2$\angle$CAB = 180° - 90°

2$\angle$CAB = 90°

$\angle$CAB = $\frac{90\°}{2}$ = 45°

Hence, the value of the angle CAB is 45°.