Question

radius of a circle is 25 cm and the distance of its chord from the centre is 4 cm what is the length of the chord?​

Answer 1

Answer:

49.34 cm is the required length of the chord .

Step-by-step explanation:

According to the Question

It is given that ,

• Radius of circle OA = 25cm
• Distance of its Chord from the centre ,BO =4cm

we need to calculate the length of the Chord.

So ,We will use here the Pythagoras Theorem .

• AO² = BO² + AB²

Substitute the value we get

➻ 25² = 4² + AB²

➻ 625 = 16 + AB²

➻ 625-16 = AB²

➻ 609 = AB²

➻ AB = √609

➻ AB = 24.67cm

As we know that distance of its Chord from the the centre is perpendicular bisector of the chord .

So, the length of the chord is twice AB

➻ Length of Chord = 2AB

➻ Length of Chord = 2×24.67

➻ Length of Chord = 49.34 cm

• Hence, the length of the chord is 49.34 cm (approx)

Answer 2

Answer:

Given :-

• The radius of a circle is 25 cm and the distance of its chord from the centre is 4 cm.

To Find :-

• What is the length of the chord.

Solution :-

First, we have to find the perpendicular :

Given :

• Radius = 25 cm [ AO ]
• Distance of its chord = 4 cm [ BO ]

Now, we have to use Pythagoras Theorem :

$\leadsto \sf\bold{\pink{AB =\: \sqrt{AO^2 - BO^2}}}$

$\implies \sf AB =\: \sqrt{(25)^2 - (4)^2}$

$\implies \sf AB =\: \sqrt{25 \times 25 - 4 \times 4}$

$\implies \sf AB =\: \sqrt{625 - 16}$

$\implies \sf AB =\: \sqrt{609}$

$\implies \sf\bold{\purple{AB =\: 24.67\: cm}}$

Now, we have to find the length of the chord :

$\longrightarrow \sf Length_{(Chord)} =\: 2 \times 24.67$

$\longrightarrow \sf Length_{(Chord)} =\: 2 \times \dfrac{2467}{100}$

$\longrightarrow \sf Length_{(Chord)} =\: \dfrac{4934}{100}$

$\longrightarrow \sf\bold{\red{Length_{(Chord)} =\: 49.34\: cm}}$

${\small{\bold{\underline{\therefore\: The\: length\: of\: the\: chord\: is\: 49.34\: cm\: .}}}}$