If the radius of a circle is 13 cm , find the length of a chord whose distance from the centre is 12 cm .

To find the length of the chord, we can use the right triangle formed by the radius, half of the chord, and the distance from the center to the chord. Here, the radius \( r = 13 \, cm \) and the distance from the center to the chord \( d = 12 \, cm \). Applying the Pythagorean theorem: \[ \text{(half of the chord)}^2 + d^2 = r^2 \] Let \( x \) be half the length of the chord. Therefore: \[ x^2 + 12^2 = 13^2 \] \[ x^2 + 144 = 169 \] \[ x^2 = 25 \quad \Rightarrow \quad x = 5 \, cm \] Thus, the full length of the chord is \( 2x = 10 \, cm \). Now you’ve got a chord length of 10 cm! Pretty neat, right? Let’s dive a little deeper! Imagine strolling along the circle’s circumference, spotting this chord! Chords are like the links connecting two points on the circle, and the closer the chord is to the center, the longer it tends to be. This relationship between the chord length and its distance from the center is a fun aspect of circle geometry—there’s always something fascinating hiding under the surface of those round shapes! 🌟