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Triangles

In a circle, ...

Question

In a circle, O is the centre and $∠ C O D$ is right-angle. AC = BD and CD is the tangent at P. What is the value of AC + CP if the radius of the circle is 1 metre?

105 cm

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141.4 cm

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138.6 cm

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can't be determined

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Solution

The correct option is B 141.4 cm

OC = OD and OA = OP = OB
OP = 1 m
$\begin{matrix} ∴ & P C = 1 M O C = \sqrt{2} m ∴ & A C = O C - O A = (\sqrt{2} - 1) m a n d & A C + C P = (\sqrt{2} - 1) + 1 = \sqrt{2} m = 1.414 m = 141.4 c m \end{matrix}$

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