NCERT · Class 10 · Mathematics · CirclesIf tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 80°, then ∠POA is equal to:
Step-by-Step Solution
In quadrilateral PAOB, sum of angles is 360°. Angle at A and B are 90° each. So ∠APB + ∠AOB = 180° ⇒ ∠AOB = 180° - 80° = 100°. Since ΔPOA ≅ ΔPOB, ∠POA = $\frac{1}{2}$ ∠AOB = 50°.
Detailed Options Breakdown
Option : 50° (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 1: 60°
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Circles.
Option 2: 70°
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Circles.
Option 3: 80°
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Circles.
💡 Study Guide: This question tests core syllabus concepts from Circles. For formulas, key summaries, and mock exam reference guides, read the full Circles Revision Notes.