From an external point, two tangents are drawn to a circle. Prove that the line joining the external point to the…
CBSE Class 10 Maths PYQ · Circles · Quad & Circle · 3 Marks · March 2023 · Standard
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1153 Marks · March 2023 · Standard
From an external point, two tangents are drawn to a circle. Prove that the line joining the external point to the centre of the circle bisects the angle between the two tangents.
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Given : PA and PB are tangents drawn from an external point P to the circle with centre O. To prove: $\angle OPA = \angle OPB\\$Construction: Join OA, OB Proof: In $\Delta OPA$ and $$\begin{aligned}& \Delta OPB \\ & OP = OP\end{aligned}$$ (common) OA = OB (radii) $\angle OAP = \angle OBP$ (each $90^\circ$, radius $\perp$ tangents) $\therefore \Delta OPA \cong \Delta OPB$ (RHS) $\Rightarrow \angle OPA = \angle OPB$ (CPCT)
