Question

Prove the given theorem:
Tangent segments drawn from an external point to a circle are congruent.
Draw radius OM and radius ON and complete the proof
of the theorem.

Answer 1

Step-by-step explanation:

Given: O is the centre of the circle. Tangents through external point P touch the circle at the points M and N. 

To prove: seg MP ≅ seg NP

Construction: Draw seg OM and seg ON.

Proof:  In ∆MOP and ∆NOP, 

seg OM ≅ seg ON [Radii of the same circle] 

seg OP ≅ seg OP [Common side]

∠OMP = ∠ONP = 90° [Tangent theorem]

  ∴ ∆OMP = ∆ONP [By Hypotenuse side test] 

∴ seg MP = seg NP [c.s.c.t]

I hope its helpful !