Question

In a circle with a 12-inch radius, find the length of a segment joining the mid-point of a 20 inch cord and the center of the circle .

Answer 1

The length of the segment is 6.63 inches

Explanation:

Given that the radius of the circle is 12 inches.

The center of the circle to the endpoint and the midpoint of the chord forms a right angled triangle.

The hypotenuse is 12 inches.

One of the sides is $\frac{20}{2}=10$

Applying the Pythagorean theorem, we have,

$a^2+b^2=c^2$

Where $a=x, b=10$ and $c=12$

Thus, we have,

$x^{2} +10^2=12^2$

Simplifying, we get,

$x^{2} =144-100$

$x^{2} =44$

Taking square root on both sides of the equation, we have,

$x=6.63$

Thus, the length of the line segment is 6.63 inches.