Question

Tp and tq are 2 tangents to a circle with center 0 ,so that angle poq=100° , find angle PTQ

Answer 1

(Diagram is given in attachment)

Given:

• TP and TQ re 2 tangents
• ∠POQ = 100°

To find:

1. ∠PTQ

METHOD:

By Tangent Perpendicularity theorem,

∠TPO = ∠OQT = 90°  → → → [Equation 1]

✰ Now we have POQT as a quadrilateral

☞ Sum of all angles in a Quadrilateral is always 360°

Applying this Concept,

∠POQ + ∠OQT + ∠PTQ + ∠TPO = 360°

⇒ 100° + 90° + ∠PTQ + 90° = 360°

⇒ 100° + 180° + ∠PTQ = 360°

⇒ 280° + ∠PTQ = 360°

⇒ ∠PTQ = 360° - 280°

⇒ ∠PTQ = 80°

∴ ∠PTQ = 80°

Additional Information:

What is Tangent Perpendicularity theorem?

➟ Tangent Perpendicularity theorem states that the angle made by the Tangent to radius of the circle is always 90°