Question

Given: OC = 1/2 OD DC is a tangent line Find: m∠DAC

Answer 1

Answer:

$\implies m\angle DAC=30\degree$.

Step-by-step explanation:

DC meets  the circle at right angles because it is a tangent.

Triangle COD is a right triangle, with OD being the hypotenuse.

$\cos m\angle COD=\frac{OC}{OD}$.

But $OC=\frac{1}{2}OD$,

$\implies \cos m\angle COD=\frac{\frac{1}{2}OD}{OD}$.

$\implies \cos m\angle COD=\frac{1}{2}$.

$\implies m\angle COD=\cos ^{-1}(\frac{1}{2})$.

$\implies m\angle COD=60\degree$.

But $m\angle DAC=\frac{1}{2} m\angle COD$.

$\implies m\angle DAC=\frac{1}{2}(60\degree)$.

$\implies m\angle DAC=30\degree$.