Question

find the length of chord which is at distance of 5cm from center of circle of radius 13cm

Answer 1

length of the chord is 24cm

Answer 2

Answer:  The required length of the chord is 24 cm.

Step-by-step explanation:  We are given to find the length of chord which is at distance of 5 cm from center of circle of radius 13 cm.

As shown in the attached figure below,  AB is a chord of a circle with center O, where

radius, OB = 13 cm and distance of AB from O, OD = 5 cm.

Since OD is the distance of AB from the center O, so it must be perpendicular to the chord AB.

So, triangle OBD is a right-angled triangle with OB as the hypotenuse.

Also, perpendicular drawn from the center of a circle to any chord bisects the chord.

That is, AD = DB.

Using Pythagoras theorem in triangle OBD, we have

$OB^2=BD^2+OD^2\\\\\Rightarrow 13^2=BD^2+5^2\\\\\Rightarrow BD^2=169-25\\\\\Rightarrow BD^2=144\\\\\Rightarrow BD=12.$

Therefore, we get

$AB=AD+BD=2BD=2\times12=24.$

Thus, the required length of the chord is 24 cm.