Question

2 a 2) In Fig 10.5 if OA= 5cm AB-8cm = , and OD is perpendicular to ÁB, then CD is equal to : ​

Answer 1

Answer:

CD = OD – OC = 5 – 3 = 2 cm

Step-by-step explanation:

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

AC = CB = 1/2 AB = 1/2 x 8 = 4 cm

given OA = 5 cm

AO2 = AC2 + OC2    

(5)2 = (4)2 + OC2

25 = 16 + OC2

OC2 = 25-16 = 9

OC = 3 cm

[taking positive square root, because length is always positive]

OA = OD [same radius of a circle]

OD = 5 cm

CD = OD – OC = 5 – 3 = 2 cm

Answer 2

Answer:

2cm

Step-by-step explanation:

Correct option is

A

2 cm

OC is perpendicular on chord AB

∴OC bisects the chord AB

⇒AC=CB

Now,

AC+CB=AB

⇒AC+CB=8

⇒AC=28

       ⇒4cm

△OCA is a right angled triangle

∴AO2=AC2+OC2

⇒52=42+OC2

⇒52−42=OC2

⇒OC2=9

⇒OC=3

Since, OD is the radius of the circle

∴OA=OD=5cm

CD=OD−OC

⇒5−3=2cm