Question

Select the correct option for the given figure and statements. Statement 1: $\Delta PBO\cong \Delta NMO$
Statement 2: $\Delta PBO\cong \Delta PQO$

• A. Both statement 1 and statement 2 are true.
• B. Statement 1 is true, while statement 2 is false.
• C. Statement 1 is false, while statement 2 is true.
• D. Both statement 1 and statement 2 are false.

Answer 1

The correct option is C Statement 1 is false, while statement 2 is true.

In$\Delta$ PBO and $\Delta$ PQO,
PB = PQ
(Tangents to a circle from an external point are equal in length.) OP = PO (Common side)
OB = OQ (Radii of the same circle)
Thus, by SSS congruence, $\Delta PBO\cong \Delta PQO$.

But,$\Delta PBO\cong \Delta NMO$.
(Since OP $\ne$ ON)

Hence, statement 1 is false, while statement 2 is true.