Question

seg RM and seg RN are tangents segment of a circle with centre O prove that seg OR bisects angle MRN as well as angle MON

Answer 1

Answer:

Step-by-step explanation:

It is given that RM and RN are the two tangent segments of a circle with centre O. Let OR be the segment and from ΔMOR and ΔNOR,

MR=NR( Tangent segments of circle are always equal)

OM=ON(Radius of the circle)

OR=OR( Common)

Therefore by SSS rule of Congruency, ΔMOR ≅ΔNOR

⇒ By CPCT,

∠MRO=∠NRO

Thus, the segment OR bisects the angle MRN

Hence proved.

Answer 2

Answer:

In ΔOMR&ΔONR

Since, OM and ON are radius of circle

So, segOM = segON

Tangents from an external point to a circle are equal in length

So, seg MR = segNR

Also seg OR = seg OR

By, side side side criterion

ΔRMO≅ΔRNO

⟹∠ORM=∠ORN

⟹∠MOR=∠NOR

Hence, the seg OR bisects ∠MRN as well as ∠MON