Question

Find the length of a which is at a distance of 5cm from the center of circle radius 10 cm​

Answer 1

Answer:

Let AB be a chord of a circle with centre O and radius 13 cm. Draw OL⊥AB. Join OA.

Here, OL=5 cm,OA=13 cm.

In right triangle OLA,

OA

2

=OL

2

+AL

2

13

2

=5

2

+AL

2

AL

2

=144

AL=12

Since the perpendicular from the centre to a chord bisects the chord. Therefore,

AB=2AL=2×12=24 cm

Step-by-step explanation:

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Answer 2

Answer:

Let O be the centre of circle and AB be the chord of the circle

Length of OC is = 5 cm

Radius of the circle OA = 10 cm

Let OCA be a delta in the given circle.

By using Pythagoras Theorem -

(OA)^2 = (AC)^2 + (OC)^2

(10)^2 = (AC)^2 + (5)^2

100 = (AC)^2 + 25

(AC)^2 = 100 - 25

(AC)^2 = 75

AC = Root 75

AC = 8.66 cm

As we know that the perpendicular from the centre to chord bisects the chord.

Therefore, AC = BC = 8.66 cm.

Therefore, the length of the chord is 8.66 + 8.66 =

17.32 cm