wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

In the given figure, if OA = 5cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to _______.

Open in App
Solution

Given:
OA = 5cm ...(1)
AB = 8 cm
OD is perpendicular to AB


We know, perpendicular from the centre to the chord bisects the chord.
Therefore, AC = CB = 12AB
⇒ AC = 4 cm ...(2)


In right angled ∆OAC,
Using pythagoras theorem
OA2 = AC2 + OC2
⇒ 52 = 42 + OC2 (From (1) and (2))
⇒ 25 = 16 + OC2
⇒ OC2 = 25 − 16
⇒ OC2 = 9
⇒ OC = 3 cm


OD = 5 cm (radius)
∴ CD = OD − OC
⇒ CD = 5 − 3
⇒ CD = 2 cm


Hence, CD is equal to 2 cm.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Circles and Their Chords - Theorem 3
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon