Question

A chord is 12 cm away from the centre of the circle of radius 15cm.find the length of the chord.

Answer 1

Answer:

Step-by-step explanation:

The radius r, distance from centre d and half the length of the chord (c/2) form a right-angled triangle with the radius r as the hypotenuse h.r^2 = d^2 + c^2 => 13^2 = 12^2 + (c/2)^2 => (c/2)^2 = 13^2 - 12^2 = 25 => (c/2) = 5. Length of the chord c = 10 cm.

Answer 2

Answer:

here,

let AB be the chord

OC=12cm. (distance of chord from centre)

OA=15cm. (radii of circle)

Since, OC perpendicular to AB

OC also bisects the chord,

AC=BC

in ∆AOC, right angled at C,

using Pythagoras theorem,

OA^2=OC^2+AC^2

15^2=12^2+AC^2

225=144+AC^2

AC^2=225-144

AC^2=81

AC=√81

AC=9cm

Therefore

length of chord = 2AC

=2*9

=18cm