UPSC CDS Math Triangles Questions

In ΔPQR,∠PQR=90°
So, a circle can be drawn passing through the points P, Q and R with PR as diameter.
∴ PT = QT = TR(Radius of the circle)
In ΔQTR
QT = TR ⇒ ∠TRQ = ∠TQR..........(1)
LM || QT
∴∠RLM = ∠TQR......(2) (Corresponding angles)
From (1) and (2), we have
∠RLM= ∠LRM (∠TRQ = ∠LRM)