Question

In a circle, O is the centre and $\angle COD$ is a 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 meter?

• A. 105 cm
• B. 141.4 cm
• C. 138.6 cm
• D. can't be determined

Answer 1

The correct option is B 141.4 cm


OC = OD and OA = OP = OB
OP = 1m
$\therefore$ PC = 1m
OC = $\sqrt{2}$m
$\therefore$ AC = OC - OA
$=(\sqrt{2}-1)m$
and AC + CP = $(\sqrt{2}-1)$ + 1
$=\sqrt{2}m$
= 1.414 m
= 141.4 cm