Prove that the angle between two tangents drawn from an external point to a circle is bisected by the line joining the external point to the centre of the circle.
Step-by-Step Solution
Key Concept: $\Delta OPT \cong \Delta OQT$ by RHS congruence $\Rightarrow \angle PTO = \angle QTO$ (CPCT) $\Rightarrow OT$ bisects $\angle PTQ$.
In $\Delta OPT$ and $\Delta OQT$, $\angle OPT = \angle OQT = 90^\circ, OT = OT, OP = OQ$. [1.5 Marks]
By RHS, $\Delta OPT \cong \Delta OQT \Rightarrow \angle PTO = \angle QTO$ (CPCT). Thus $OT$ bisects $\angle PTQ$. Proved! [1.5 Marks]
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🎯 Official CBSE Marking Scheme:
Proving RHS congruence of $\Delta OPT$ and $\Delta OQT$: 1.5 Marks
Concluding $\angle PTO = \angle QTO$: 1.5 Marks
Correct Answer: