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  • In Fig. 10.3, if OA equal to 5 cm, AB equal to 8 cm and OD is perpendicular to AB, then CD is equal to: (A) 2 cm (B) 3 cm (C) 4 cm (D) 5 cm

In Fig. 10.3, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to:

Fig. 10.3

(A) 2 cm

(B) 3 cm

(C) 4 cm

(D) 5 cm

Answers (1)

We know that the perpendicular from the centre of a circle to a chord bisects the chord.

AC = CB = \frac{1}{2} AB = \frac{1}{2} \times 8 = 4 cm

Given OA = 5 cm

Using Pythagoras theorem,

\\AO^{2} = AC^{2} + OC^{2}\\ (5)^{2} = (4)^{2}+ OC^{2}\\ 25 = 16 + OC^{2}\\ OC^{2} = 25 - 16 = 9\\ OC = 3 cm\\

(Taking positive square root, because length is always positive)

OA = OD         (same because both are radius)

OD = 5 cm

CD = OD – OC = 5 – 3 = 2 cm

Therefore option (A) is correct.

Posted by

infoexpert24

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