Question

In O (P.r) a chord of 20cm length is 24cm away
from the centre. Find the length of a chord which
is at distance 10 from the centre.​

Answer 1

Answer:

48 cm

Step-by-step explanation:

Drop a perpendicular on the 20cm chord from the centre.

Note that this is a right-angled triangle and length of the base is 20/2 = 10cm and hypotenuse is the radius of the circle.

Applying Pythagoras theorem,

⇒ radius^2 = 10^2 + 24^2

⇒ radius^2 = 576 + 100 = 676

Now, again drop a perpendicular on the 2nd chord from the centre. Let the length of the chord be "a". Then, base of triangle = a/2.

⇒ radius^2 = (a/2)^2 + 10^2

⇒ 676 = (a/2)^2 + 100

⇒ 576 = (a/2)^2

⇒ 24 = a/2

⇒ 48 = a

    Length of the chord is 48 cm

Answer 2

Given

• Chord length = 20 cm
• Distance from which it is away from the centre = 24 cm

To find

• Length of chord which is at a distance 10 cm from the centre

Solution

Here, a right angled triangle is inscribed in a circle.

So, the length of base will be 20/2 = 10 cm

Now, we have lengths of two sides and we shall find the hypotenuse, that is the radius, using Pythagoras theorem.

• r² = 10² + 24²
• r² = 100 + 576
• r² = 676
• r = √676
• r = 26

Hence, we get the radius to be 26 cm

Now, a construction shall be done here, draw a perpendicular on the other chord from the circle, then length of chord will be a and since it is a right angled triangle, the base will be a/2.

So, similarly let's find the radius or hypotenuse using Pythagoras theorem.

• r² = (a/2)² + 10²  (a) is distance
• 576 = (a/2)² + 100
• (a/2)² = 676
• Square root on both the sides,
• √(a/2)² = √676
• 24 = a/2
• a = 24 × 2
• a = 48

Hence, the length of the chord is 48 cm