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

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Answer 1

Explanation:

Given :-

• Radius of circle is =13 cm
• distance of chord ab from centre P is 5 cm

To Find :-

• what is the length of chord AB ?

Solution :-

late 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.

• Perpendicular = 5Cm
• Hypotenuse= 13Cm

applying Pythagoras theorem,

➟ (Ap )² = ( AL )² + ( PL ) ²

➟ ( 13 )² = ( AL )² + ( 5 ) ²

➟ ( AL )² = ( 13 )² - ( 5 )²

➟ AL² = 144

➟ AL = √144

➟ AL = 12Cm

Since, PL is perpendicular to line ab So,

• AL = LB

➟ AB = AL + LB

➟ AB = 12 + 12

➟ AB = 24Cm

Hence ,the length of the chord AB is

=24 cm

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Answer 2

Explanation:

24 cm

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