Question

PQ is the perpendicular bisector of AB. Then which of the following are correct?

• A. AP = BP
• B. AP = BQ
• C. $\angle AOP$ = $\angle BOP$
• D. OB = OP

Answer 1

Answer: (A), (B), (C)

The correct options are
A AP = BP
B AP = BQ
C $\angle AOP$ = $\angle BOP$

Given
PQ is the perpendicular bisector of AB.
$\Rightarrow$$\angle AOP$ = $\angle BOP$ = ${90}^{\circ }$.

During construction, arcs are dawn on either side of AB with the same radius
$\Rightarrow$ AP = AQ
With the same radius and taking B as centre another two arcs are drawn to cut the previous arcs at P , Q .
$\Rightarrow$ AP = AQ = BP = BQ (Equal radii)

$\therefore$ AP = BP and AP = BQ is also true.