Question

In a circle of radius 5 cm having centre O, OL is drawn perpendicular to the chord AB. If OL=3cm, find the length of AB

Answer 1

Answer:

6 cm

Step-by-step explanation:

hope the pic helps

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Answer 2

Given:

• The radius of the circle = 5 cm
• OL is perpendicular to chord AB.
• The length OL = 3 cm

To Find:

• The length of AB.

Solution:

First, let us construct a figure using the given data.

Since the radius is given as 5 cm therefore in the figure OB = 5cm.

From the figure, we can say that,

We know that perpendicular drawn to the chord from the center bisects the chord itself, therefore, AL = LB

We gat a triangle OLB from the figure which is a right-angled triangle at point L.

∴ ∠OLB = 90°

On applying Pythagoras theorem in ΔOLB we get,

⇒ $OB^2=OL^2+LB^2$  ( rearranging the terms in order to get the value of LB)

⇒ LB = $\sqrt{OB^2-OL^2}$ → {equation 1}

Substitute the given values in equation 1,

⇒ LB = $\sqrt{5^2-3^2}$ =  √(25-9)

⇒ LB = √16 = 4 cm

So, the length of the chord,

AB = 2(LB) = 4×2 = 8cm

∴ The length of the chord AB = 8 cm.