Question

if the length of a chord of a circle at the distance of 5cm from the center of the circle is 24cm , find the radius

Answer 1

Answer:

26 cm

Step-by-step explanation:

assume the circle radius and chord as ABCD.

Given 24 cm and OC=5 cm

Since, the perpendicular from the centre of the circle to the chord bisects the chord,

AC=CB=12 cm

Join, OA, in △AOC

AO

2

=AC

2

+OC

2

(PythagorasTheorem)

=12

2

+562

=144+25=169

⇒AO=

169

=13cm

∴Diameter=2×=2×AO=2×13cm=26cm

Answer 2

Answer: Radius of circle is 13 cm

Step-by-step explanation:

Given,

BC=24 cm and OA=5 cm

Since, the perpendicular from the center of the circle to the chord bisects the chord

BA=AC=12cm

$OB^{2} =OA^{2} +AB^{2} \\=5^{2} +12^{2}$

=$\sqrt{5^{2}+12^{2} }$

=$\sqrt{169}$

=13 cm

Diameter of circle i=2*radius

=2*13

=26 cm

Hence, Radius of circle is 13 cm

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