Join OP and OQ. In OPS and OQS: OP=OQ……Radius of circle OPS=OQS=900 (Tangent is to the radius through the point of contact) OS=OS….common Therefore, by Right angle-Hypotenuse-Side criterion of congruence, we have
OPS OQS (RHS) The corresponding parts of the congruent triangles are congruent.
POS = QOS……cpct, OSP = OSQ ……..cpct In quadrilateralPSQO: POQ+PSQ=1800 as the total sum of interior angles in a quadrilateral=3600 POQ=PSQ=900 So OSP = OSQ = 45oAs PSQ=900 STC=900 sum of two co interior angles is 180 o.
SOT is an isosceles triangle having two sides: OS=OT Similarly, QOT = 45o SOT = 90o
Regards 
OPS and 
OPS=
to the radius through the point of contact)
