CBSE2026Class Class 10 · Mathematics1 Marks · Mcq✅ Verified
In the given figure, $PT$ is a tangent to the circle with centre $O$ and radius $r$. If $\angle POT = 45^\circ$, then the length of $OP$ is :
A. $r\sqrt{2}$
B. $\sqrt{2r}$
C. $2r$
D. $r^2$
✅ Answer & Solution
✅ Correct Answer: A
Step 1: Radius $\perp$ tangent at point of contact, so $\angle OTP = 90^\circ$.
Step 2: In right $\triangle OTP$,
$$\cos 45^\circ = \frac{OT}{OP} = \frac{r}{OP}$$
Step 3: $$\frac{1}{\sqrt{2}} = \frac{r}{OP} \Rightarrow OP = r\sqrt{2}$$
