Question

A chord of a circle of radius 5cm subtends a right angle at its centre. The lenght of chord in cm is

Answer 1

Answer:

The length of the required chord is 7.07cm.

Step-by-step explanation:

Given that,

A chord of a circle of radius 5cm subtends a right angle at its center and

we are required to find the length of the chord.

In the given figure we have

Radius=OA=OB=5cm

And we are required to find the measure of chord AB.

Using the Pythagorean theorem we write,

$OA^2+OB^2=AB^2\\= > 5^2+5^2=AB^2\\= > AB=\sqrt{50}=7.07cm$

Therefore,

The length of the required chord is 7.07cm.

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Answer 2

Answer:

Length of the chord =  5$\sqrt{2}$cm

Step-by-step explanation:

Given,

A chord of a circle of radius 5cm subtends a right angle at its center.

To find,

The length of the chord

Solution:

Let AB be the chord and 'O' be the center of the circle.

Since Chord is a line segment joining any two points of a circle, we have OA and OB are radii of the circle

Since it is given that the radius of the circle is 5cm we have,

OA = OB = 5cm

Also, we have the chord AB subtends a right angle at the center, we have

ΔOAB is a right-angled triangle with ∠AOB = 90°

AB is the hypotenuse of the triangle ∠AOB

Then, by Pythagoras theorem, we have

AB² = OA² + OB²

AB² = 5² + 5²

= 25+25

= 50

AB = $\sqrt{50}$ = 5$\sqrt{2}$cm

∴ Length of the chord =  5$\sqrt{2}$cm

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