CBSE2026Class Class 10 · Mathematics1 Marks · Mcq✅ Verified
In the given figure, if $AB$ is a tangent to the circle with centre $O$ such that $OB=6$ cm and $\angle AOB=60^{\circ}$, then the length of $OA$ is : (Here $B$ is the point of contact and $A$ is an external point.)
A. $3$ cm
B. $3\sqrt{3}$ cm
C. $4\sqrt{3}$ cm
D. $12$ cm
✅ Answer & Solution
✅ Correct Answer: D
Step 1: The radius through the point of contact is perpendicular to the tangent, so $\angle OBA=90^{\circ}$.
Step 2: In right $\triangle OBA$, $OB=6$ cm is the side adjacent to $\angle AOB=60^{\circ}$ and $OA$ is the hypotenuse.
Step 3: Use the cosine ratio.
$$\cos 60^{\circ}=\frac{OB}{OA}$$
Step 4: Substitute $\cos 60^{\circ}=\dfrac{1}{2}$.
$$\frac{1}{2}=\frac{6}{OA}$$
Step 5: Therefore $OA=12$ cm.
Correct option is (D) 12 cm.
