Question

PQRS is a square M is the midpoint of PQ & RM $\perp$ AB.
then RA = RB

• A. True
• B. False

Answer 1

The correct option is A True

Given PQRS is square and M is midpoint of PQ

Also $RM\perp AB$

In $△APM$ and BMQ

$PM=MQ\angle APM=\angle BQM={90}^0\angle AMP=\angle BMQ$[Vertically opp.]

$A{R}^2=A{M}^2+R{M}^{2}A{R}^2=M{B}^2+R{M}^2$

similarly $B{R}^2=M{B}^2+R{M}^{2}A{R}^2=B{R}^2$

Hence, AR = BR