Question

Radius of a circle with center 0 is 10cm Find the lenght of the chord if the chord is at a distance of 6cm From the centre.​

Answer 1

Step-by-step explanation:

?

O is the centre of circle, radius of the circle=OA=r=10 cm, AB = ?, OC = 6 cm, C is point on chord AB & OC perpendicular to AB.

Now, In right triangle OAC,

By Pythagoras Theorem

OA ² = AC² + CO²

Or, AC² = OA² - CO²

Or, AC² = 10² - 6² = 100 - 36 = 64

Or, AC² = 100 - 36

Or, AC² = 64

Or, AC² = 8²

Or, AC = 8

Or AB = AC + CB

Or AB = 8 + 8 ----------- (AC = CB)

Or AB = 16 cm

Therefore, length of chord = AB = 16 cm

Answer 2

Step-by-step explanation:

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