MCQ
Write the correct answer in the following: In Fig. if $OA = 5\ cm, AB = 8\ cm$ and $OD$ is perpendicular to $AB$, then $CD$ is equal to: 
- A$2\ cm$.
- B$3\ cm$.
- ✓$4\ cm$.
- D$5\ cm$.
✓
Answer
Correct option: C.
$4\ cm$.
As perpendicular from the centre to a chord the chord,
$\text{AC}=\frac{1}{2}\times\text{AB}=\frac{1}{2}\times8=4\text{cm}$
$\text{OC}=\sqrt{(\text{OA})^2-(\text{AC})^2}=\sqrt{(5)^2-(4)^2}=\sqrt{25-16}=\sqrt{9}$
$OC = 3\ cm$
Now, $CD = OD - OC$
$= 5\ cm - 3\ cm = 2\ cm$
Hence, $(c)$ is the correct answer.
$\text{AC}=\frac{1}{2}\times\text{AB}=\frac{1}{2}\times8=4\text{cm}$
$\text{OC}=\sqrt{(\text{OA})^2-(\text{AC})^2}=\sqrt{(5)^2-(4)^2}=\sqrt{25-16}=\sqrt{9}$
$OC = 3\ cm$
Now, $CD = OD - OC$
$= 5\ cm - 3\ cm = 2\ cm$
Hence, $(c)$ is the correct answer.
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