In a circle radius rcm, a chord 16\(\sqrt{3}cm\) long is 10cmfrom the centre of the circle. Find, correct to the nearest cm, the value of r
Answer Details
In a circle, a radius is a line segment that connects the center of the circle to any point on the circle. A chord is a line segment that connects two points on a circle.
Given that a chord of length 16\(\sqrt{3}cm\) is 10cm from the center of the circle, we can use the Pythagorean theorem to find the length of the radius.
First, we draw a line from the center of the circle perpendicular to the chord, creating a right triangle with the radius, the perpendicular line, and half the chord length (which is \(8\sqrt{3}\) cm).
Using the Pythagorean theorem:
\begin{align*}
r^2 &= (8\sqrt{3})^2 + 10^2 \\
r^2 &= 192 + 100 \\
r^2 &= 292 \\
r &\approx \sqrt{292} \\
r &\approx 17 \text{ cm}
\end{align*}
Rounding to the nearest whole number, we get the answer of 17cm. Therefore, the correct option is (b) 17cm.