Question

In a circle of radius 13cm,a chord of a distance 5cm from the centre. Find the length of the chord?

Answer 1

Answer:

24 cm

Step by Step Explanation :

Given :

radius of circle = 13 cm

distance of chord from centre = 5 cm

Construction : Draw a circle with centre O. Join the radius of the circle to one end of the chord AB . Draw a perpendicular from centre of the circle to the chord. Name the point of intersection as C. Now a triangle OCB is formed

Solution : Using Pythagoras theorem in triangle OCB,

13×13 = 5 × 5 + CB × CB

169 = 25 +CB x CB

169 - 25 = CB x CB

144 = CB x CB

12 = CB

Therefore, Length of chord = 2 x 12 = 24 cm.

Based on the theorem the perpendicular line joining the centre of the circle to the chord bisects the chord.

Answer 2

Step-by-step explanation:

Let AB be the chord of a circle of radius 13 cm at a distance of 5cm from centre O.

Then, OA=13xm, OM=5cm

Using Pythagoras theorem,

OA²=OM²+AM²

i.e.,.

${13}^{2} = {5}^{2} + {am}^{2}$

or

${AM}^{2} = {13}^{2} - {5}^{2}$

$= 169 - 25 = 144$

$AM = 12$

$AB = 2 \times 12 = 24cm$

perpendicular perpendicular from centre bisector of chord

length of the chord = 24 cm