Question

can you answer this question please and fast

Answer 1

Solution :-

Given -

OA = 5 cm, AB = 8 cm and OD is perpendicular to AB.

CD = ?

As, it is clear from the figure that OA (which is radius of the given circle) = OD = 5 cm

And, 

AB = 8 cm, is a chord of the given circle.

A line from the center to the chord is the perpendicular bisector.

AC = CB = 1/2 of AB

⇒ 1/2 × 8 = 4 cm

So, AC = CB = 4 cm 

Using Pythagoras Theorem -

(Hypotenuse)² = (Base)² + (Perpendicular)²

⇒ (OA)² = (AC)² + (OC)²

⇒ (5)² = (4)² + (OC)²

⇒ 25 = 16 + (OC)²

⇒ (OC)² = 25 - 16

⇒ (OC)² = 9

⇒ OC = √9

⇒ OC = 3 cm

As, OA = OD = 5 cm

Then, 

CD = OD - OC

CD = 5 - 3

CD = 2 cm

So, the length of CD is 2 cm

Answer.