Mathematics: Given: oc = 1/2 od dc is a tangent line find: m∠dac

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Given: oc = 1/2 od dc is a tangent line find: m∠dac

Ответ:

mgavyn9457

17.01.2022

Mathematics

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

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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Given: oc = 1/2 od
dc is a tangent line
find: m∠dac

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