# How to find the radius of a circle with a chord?

In a circle, the distance from the center point of a circle to its circumference or any endpoint on the circle is called the radius of a circle. It can also be defined as the length of the line segment from the center of a circle to a point on the circumference of a circle.

## Answer: The radius of a circle with a chord is r=√(l^{2}+4h^{2}) / 2, where 'l' is the length of the chord and 'h' is the perpendicular distance from the center of the circle to the chord.

We will use Pythagoras theorem to find the radius of a circle with a chord.

**Explanation:**

We know that,

The line which joins the center of a circle to the midpoint of a chord is perpendicular to the chord.

Let the length of the chord be **l** and the distance from the center of the circle to the chord be h as shown in the figure below.

Now, we apply Pythagoras theorem,

Hypotenuse = √( height^{2} + base^{2})

⇒ r = √[h^{2}+(l/2)^{2}]

⇒ r = √ [h^{2}+(l^{2}/4)]

⇒ r = √(l^{2}+4h^{2}) / 2

### Hence, the radius of a circle with a chord is r = √(l^{2}+4h^{2}) / 2.

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