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The diameter of a circle with centre at C is 50 cm. CP is a radial segment of the circle. AB is a chord perpendicular to CP and passes through P. CP produced intersects the circle at D. If DP = 18 cm, then what is the length of AB?

A) 24 cm
B) 32 cm
C) 40 cm
D) 48 cm

Correct Answer:




D) 48 cm

Description for Correct answer:

In \( \Large \triangle ACP, \)

\( \Large CP = CD - PD = 25 - 18 = 7 \)

Now, \( \Large AC^{2} = CP^{2} + AP^{2} \)

\( \Large \therefore AP = \sqrt{AC^{2}-CP^{2}} = \sqrt{ \left(25\right)^{2} - \left(7\right)^{2} } \)

= \( \Large \sqrt{625-49} = \sqrt{576} = 24 cm \)

Similarly, PB = 24 cm

Therefore, AB= AP + PB = 24 + 24 = 48 cm

Part of solved Geometry questions and answers : >> Elementary Mathematics >> Geometry

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