Question

In the above figure, PB and PQ are tangents from point P, and MN and RN are tangents from the point N to the circle with centre O.

Select the statemeents that are true:

• A. $\Delta PBO\cong \Delta MON$
• B. $\Delta PBO\cong \Delta PQO$
• C. $\Delta NOM\cong \Delta POQ$
• D. $\Delta MON\cong \Delta RON$

Answer 1

Answer: (B), (D)

The correct options are
B

$\Delta PBO\cong \Delta PQO$

D

$\Delta MON\cong \Delta RON$

In $\Delta MON$ and $\Delta RON$

OM = OR [Radius of the same circle]
MN = QR [Tangents to a circle from the same point are equal]
ON = ON [Common side]

$\therefore \Delta MON\cong \Delta RON$ [Through SSS congruency rule]

Similarly, $\Delta PBO\cong \Delta PQO$