MCQ
In a circle with centre $O, AB$ and $CD$ are two diameters perpendicular to each other. The length of chord $AC$ is:
- A$2\text{AB}$
- B$\sqrt{2}$
- C$\frac{1}{2}\text{AB}$
- ✓$\frac{1}{\sqrt{2}}\text{AB}$
✓
Answer
Correct option: D.
$\frac{1}{\sqrt{2}}\text{AB}$
$OC = OA = r ($radius$)$
$AB =$ Diameter $= 2r$
$\text{AC}=\sqrt{(\text{OA})^2+(\text{OC})^2}$
$=\sqrt{\text{r}^2+\text{r}^2}$
$=\sqrt{2}\text{r}$
$=\sqrt{2}\Big(\frac{\text{AB}}2{}\Big)$
$\Rightarrow\text{AC}=\frac{1}{\sqrt2}\text{AB}$
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