In the given figure, AB and CD are tangents to a circle centred at O. Is $∠ B A C = ∠ D C A$ Justify your answer.

Question

In the given figure, AB and CD are tangents to a circle centred at O. Is $∠ B A C = ∠ D C A$ ? Justify your answer.

Smart Achievers · Accepted Answer

Tangent to a circle from an external point are equal

RA = RC

So, $∠ R A C = ∠ R C A$

Let $∠ R A C = ∠ R C A = x$

We know that BAR and DCR are straight line.

$∠ B A C + ∠ C A R = 180 ⁰$

$\Rightarrow ∠ B A C + x = 180 ⁰$

$\Rightarrow ∠ B A C = 180 ⁰ - x$

Similarly, $∠ D C A = 180 ⁰ - x$

So $∠ B A C = ∠ D C A$

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