In a circle of radius $12\text{cm}$, a chord subtends a central angle of $90^{\circ }$. Find the length of this chord. Give your answer in centimeters, rounded to two decimal places.

Step-by-step solution

1. Step 1: Recall the formula for the length of a chord: c = 2rsinleft(\frac{\theta}{2}\right), where $\theta$ is in degrees.
2. Step 2: Substitute $r=12\text{cm}$ and $\theta =90^{\circ }$ into the formula.
3. Step 3: Compute $\frac{\theta }{2}=\frac{90}{2}=45^{\circ }$.
4. Step 4: Evaluate $sin45^{\circ }=\frac{\sqrt{2}}{2}\approx 0.70710678$.
5. Step 5: Multiply: $2\times 12\times 0.70710678=24\times 0.70710678\approx 16.9705626$.
6. Step 6: Round to two decimal places: $16.97\text{cm}$.

Concept tested: Chord length formula

Published 7 October 2026 · How this solution was prepared and checked