Question

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

Answer 1

See below

Explanation:

Actully, incase some people input it wrong, the answer is 30 degrees. DEGREES<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

so input 30 degrees

Answer 2

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

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=(OC)/(OD)`.

But
`OC=(1)/(2)OD`,

`\implies \cos m\angle COD=((1)/(2)OD)/(OD)`.

`\implies \cos m\angle COD=(1)/(2)`.

`\implies m\angle COD=\cos ^(-1)((1)/(2))`.

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

But
`m\angle DAC=(1)/(2) m\angle COD`.

`\implies m\angle DAC=(1)/(2)(60\degree)`.

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