Question

The distance of a chord from the centre of circle is 4cm. If the radius is 5cm. Calculate the length of the chord
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Answer 1

Question: The distance of a chord from the centre of circle is 4cm. If the radius is 5cm. Calculate the length of the chord

Answer:☝

Answer 2

Let the Centre of the circle be O

and Chord be PQ

Let the The distance of a chord from the centre of circle is OR

Given:-

• Radius of the circle (OP) = 5cm
• The distance of a chord from the centre of circle is (OR) 4cm.

To Find:-

• Lenght of the chord PQ

Information:-

* The Perpendicular drawn from the centre bisects the chord into 2 equal parts

Solution:-

In Triangle OPR

${op}^{2} = {or}^{2} + {pr}^{2}$

By Pythagoras Theorem

So,

${5cm}^{2} = {4cm}^{2} + {pr}^{2}$

$= > {pr}^{2} = {5cm}^{2} - {4cm}^{2}$

$= > {pr}^{2} =25 {cm}^{2} - 16 {cm}^{2}$

$= > {pr}^{2} = 9 {cm}^{2}$

$= > pr = \sqrt{9 {cm}^{2} }$

$= > pr = \sqrt{3 \times 3} cm$

$= > pr = 3cm$

We Know that

$2 \times pr = pq$

So,

Substituting the value of PR

$2 \times 3cm = pq$

$= > pq = 6cm$