In the given figure, AT is tangent to a circle centred at O. If $∠ C A T = 40 °$ , then $∠ C B A$ is equal to

Question

Smart Achievers · Accepted Answer

(4)

Given, $∠ C A T = 40 °$

$∠ B A T = 90 °$

$\Rightarrow ∠ B A C + ∠ C A T = 90 °$

$\Rightarrow ∠ B A C = 50 °$

$\Rightarrow ∠ A C B = 90 ° [Angle in semi-circle]$

$In ∆ A B C, ∠ A + ∠ B + ∠ C = 180 °$

$\Rightarrow 50 ° + ∠ B + 90 ° = 180 °$

$\Rightarrow ∠ B = 180 ° - 140 ° = 40 °$

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