Question

AB is a chord of a circle at a distance 5 cm from the centre. If the length of the chord is 24 cm then the radius is ?​

Answer 1

Radius = 13cm

{A straightforward piece of congruent-triangle figuring establishes that the perpendicular meets the line at its midpoint (dividing the 24cms into two halfs that is 12cm each.So you will have a pair of right-angled triangles with sides of 5 and 12 adjacent to the right angle. The third side is the radius of the circle.

x²= 5²+12²  

x²= 25+144

x²= 169

x=√169

x= 13cm

Radius of the circle is 13cm.

Answer 2

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using Pythagoras theorem..

Distance between the cord and the center is 5 cm which is equals to its perpendicular of the triangle.

Half length if the cord which is 24/2 cm which is 12 cm is the Base of the triangle.

and the Radius is the hypotenuse.which we have to find .

so NOW-->

${h}^{2} = {p}^{2} + {b}^{2}$

${Radius}^{2} = {5}^{2} + {12}^{2} \\ {Radius}^{2} = 25 + 144 \\ {Radius}^{2} = 169 \\ {Radius} = \sqrt{169} \\ Radius = 13 \: \: cm \: \: \: \: ans...$

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