Question

radius of a circle of is 10 cm. find the length of the chord if the chord is at a distance of 6 cm from the centre​

Answer 1

Let the circle be with center O and radius 10 cm. Let there be a chord AB
Draw a perpendicular from O on AB to meet at P. The perpendicular from the center divides the chord in two halves. Given, OP=6cm
Thus, In △OAP, Using Pythagoras theorem
OA
2
=AP
2
+OP
2

10
2
=AP
2
+6
2

AP
2
=64
AP=8 cm
Thus, AB=2AP=16 cm
Now, new chord CD is drawn with length 8 cm. Draw a perpendicular on CD from O to cut CD at N.
Now, In △ONC
OC
2
=NC
2
+ON
2

10
2
=4
2
+ON
2

ON=
84
​
cm

Answer 2

MARK ME AS THE BRAINLIEST

Answer:

AB = 16 cm

Step-by-step explanation:

HERE:

OB is radius = 10

OC is the perpendicular distance from the chord to the centre of the circle = 6

AB is the given chord

TO FIND THE LENGTH OF THE CHORD

by pythagoras theorem

OC^2 + BC^2 = OB^2

6^2 + BC^2 = 10^2

BC^2 = 100 - 36 = 64

SO, BC = √64 = 8

We know that perpendicular bisector divides the chord into two equal parts

BC = AC = 8

BC + AC = 8 + 8

AB = 16 cm

HOPE IT IS USEFUL