Prove that the line segment joining the points of contact of two parallel tangents to a circle is a diameter of the circle.
Step-by-Step Solution
Key Concept: Let tangents at $A, B$ be parallel. Radii $OA \perp L_1, OB \perp L_2$. Since $L_1 \parallel L_2$, $\angle OAL_1 + \angle OBL_2 = 180^\circ \Rightarrow AOB$ is a straight line $\Rightarrow AB$ is a diameter.
$\angle OAL_1 = 90^\circ$ and $\angle OBL_2 = 90^\circ$. [1.0 Mark]
Since $L_1 \parallel L_2$, consecutive interior angles $\angle AOB = 180^\circ \Rightarrow A-O-B$ is a straight line. $AB$ is a diameter. Proved! [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Stating perpendicular radii: 1.0 Mark
Showing $A-O-B$ is a straight line of length $2r$: 1.0 Mark
Correct Answer: