In Fig. 10.3, if OA = 5 cm, AB = 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

Solution:

We know that

Perpendicular from the centre of a circle to a chord bisects the chord

AC = CB = 1/2 AB

= 1/2 × 8

= 4 cm

It is given that

OA = 5 cm

Using the Pythagoras theorem

AO² = AC² + OC²

Substituting the values

5² = 4² + OC²

OC² = 25 - 16

OC² = 9

OC = 3 cm

As the radius of the circle is same OA = OD

OD = 5 cm

CD = OD - OC

= 5 - 3

= 2 cm

Therefore, CD is equal to 2 cm.

✦ Try This: If OA = 6 cm, AB = 9 cm and OD is perpendicular to AB, then CD is equal to:

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 10

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NCERT Exemplar Class 9 Maths Exercise 10.1 Problem 2

In Fig. 10.3, if OA = 5 cm, AB = 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

Summary:

In Fig. 10.3, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to 2 cm

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