Question

In a circle with center P and radius 13 cm, the distance of chord AB from center P is 5 cm. Then,
AB=
cm.
a) 5
b) 12
c) 24
d) 8​

Answer 1

Given:–

• Radius of the circle = 13 cm
• Distance of chord AB from center P is 5 cm.

To Find:–

• What is the length of chord AB ?

Solution:–

Let AB be a chord inside a circle and AP is radius of the circle.

Construction:–

• Draw a line PL perpendicular to AB.

Calculation:–

In the circle, APL is a right-angled triangle.

• $\bf{Perpendicular = \rm{5 \: cm}}$
• $\bf{Hypotenuse = \rm{13 \: cm}}$

Applying Pythagoras theorem,

$\rm\orange{\implies (AP)^2 = (AL)^2 + (PL)^2 }$

$\rm\orange{\implies (13)^2 = (AL)^2 + (5)^2}$

$\rm\orange{\implies (AL)^2 = (13)^2 - (5)^2}$

$\rm\orange{\implies AL^2 = 169 - 25}$

$\rm\orange{\implies AL^2 = 144}$

$\rm\orange{\implies AL = \sqrt{144}}$

$\implies\red{\underline{\underline{\bf{ \: \: AL = 12 \: cm \: \: }}}}$

Since, PL is perpendicular to line AB so,

• AL = LB

$\rm\orange{\implies AB = AL + LB}$

$\rm\orange{\implies AB = 12 + 12}$

$\implies\red{\underline{\underline{\bf{ \: \: AB = 24 \: cm \: \: }}}}$

❛ Hence, The length of the chord AB is 24 cm ❜

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Answer 2

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Corrected Question :-

• In a circle with center P and radius 13cm, the distance of chord AB from center P is 5cm. Then, AB=

Answer :-

Given :-

• Radius of circle = 13cm
• Distance of chord AB from center P is 5m

To Find :-

• Length of AB.

Construction :-

• Draw a line PL perpendicular to AB.

Solution :-

Let AB be a chord inside a circle and AP is radius of the circle.

• In the right angled triangle APL, using Pythagoras theorem.

$\sf {(AP)}^{2} = {AL}^{2} + {PL}^{2}$

$\sf {(13)}^{2} = {AL}^{2} + {(5)}^{2}$

$\sf \: {AL}^{2} = {(13)}^{2} - {(5)}^{2}$

$\sf {AL}^{2} = 169 - 25$

$\sf {AL}^{2} = 144$

$\sf \: AL = \sqrt{144}$

$\sf \: AL = 12cm$

Since PL is perpendicular to SO.

• AL = LB
• LB = 12m

AB = AL + LB

AB = 12cm + 12cm

$: \implies { \underline{ \boxed{ \mathfrak{ \pink{AB = 24cm}}}}}$

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$\rm{ \color{cyan}{❤||ur \: shona||❤}}$