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notsponge [240]
4 years ago
6

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

Mathematics
1 answer:
jenyasd209 [6]4 years ago
3 0

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.

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