Question

the diameter of a circle is 26 cm and a chord is perpendicular to a radius at a point 5 cm from the center. what is the length of the radius?

Answer 1

Answer:

Step-by-step explanation:

Diameter = 26 cm (given)

Radius = Diameter/2 = 26/2 = 13cm

Answer 2

Answer:

Given,

Diameter of circle = 26 cm

Radius of circle = D / 2 => 26 /2 = 13 cm.

from the center of the circle O draw a perpendicular on to the cord AB

Let it meet the cord at P.

PO = 12cm

The chord meet the circle at A and B. Join AO. then AOP is a right triangle in which

OA = 13cm (Hypotenuse)

OM = 12 cm (Distance of the chord from the centre of the circle)

PA = Half chord length    

We Know,

$OA^{2} - OP^{2} = PA^{2}$

$13^{2} - 12^{2} = PA^{2}$

$PA^{2} = 169 - 144$

=>  $\sqrt{25}$cm

=>  $PA^{2} = 5 cm$

There fore  length of chord = 2× 5 = 10 cm.

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@GauravSaxena01