Given line AP and AS are tangent to point O at P and S respectively. Prove line segment AO is perpendicular to line segment PS

Question

How to solve geometry proof when determining two segments are perpendicular.

Answer 1

I think you have not supplied the problem correctly and but I will take a chance that what you meant is that the lines AP and AS ar tangent to a circle with center O.

 

∠APO = ∠ASO = right angle because the lines are tangents

This means ΔAPO is congruent to ΔASO

Call the intersection of AO and SP point D

ΔSDO is congruent to ΔPDO by SAS

Therefore supplemental angles SDO and PDO are equal and therefore right angles

QED