# In Fig. 10.62, <i

To prove: PQ and OT are the right bisectors.

Proof:

To prove PQ and OT are the right bisectors,

We need to prove ∠PRT= ∠TRQ=∠QRO=∠ORP = 90º

As it is given that ,

⇒ ∠POQ = 90º

In Δ POT and  Δ OQT

∠OPT = ∠OQT = 90º ( Tangent to a circle at a point is perpendicular to the radius through the point of contact)

OT=OT (common)

∴ Δ POT ≅ Δ OQT

Thus PT=OQ ( BY C.P.C.T)  ..... (1)

Now in Δ PRT and Δ ORQ

∠TPR = ∠OQR ( alternate angles)

∠PTO = ∠TOQ (alternate angles)

PT=OQ ( from (1) )

∴ Δ PRT ≅ Δ ORQ

Thus TQ = OP ( By C.P.C.T 0

Hence PT=TQ=OQ=OP

Thus it is a square,

⇒ The diagnols bisect at  90º.

Hence proved

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Area Related to Circles- Important Formula and Concepts59 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses