Question

32. The radi of two concentric circles are 13 and 8. A chord of the outer circle touches
the inner circle. Find the length of that chord.(with diagram)​

Answer 1

Answer:

2√105

Step-by-step explanation:

Let the length of the chord be 'x'.

In the formed triangle, base = x/2.

 Using Pythagoras theorem,

⇒ 13² = 8² + (x/2)²

⇒ 169 - 64 = (x/2)²

⇒ √105 = x/2

⇒ 2√105 = x

Length of the chord is 2√105 unit.

Note that, if the radius of the inner circle is 5.

(x/2)² = 169 - 25 = 144

x = 24 unit = length of chord

Answer 2

Given :-

Radii of two concentric circle = 13 and 8 cm

To Find :-

Length of chord

Solution :-

Let the chord be y

We know that base is half of chord.

Base = y/2

By using Pythagoras theorem

13² = 8² + (y/2)²

169 = 64 + y²/4

169 - 64 = y²/4

105 = y²/4

105 × 4 = y²

420 = y²

2√105 = y