Question

In the given figure, DF is an arc of a circle having radius r. If AD = AF = DF = r and $DE=\frac{3}{4}DF$, then the measure of ∠CAB is

• A.
  15°
• B.
  30°
• C.
  45°
• D.
  22.5°

Answer 1

The correct option is C

45°
Since AD = AF = DF = r.
∴ ∠FAD = 60°
Now, $DE=\frac{3}{4}DF$
$\Rightarrow \angle EAD=\frac{3}{4}\angle FAD$
$\Rightarrow \angle EAD=\frac{3}{4}\times {60}^{\circ }={45}^{\circ }$
∴ ∠CAB = 45° (∵ ∠CAB = ∠EAD)
Hence, the correct answer is option (c).