Question

plz solve this similarity problem

Answer 1

In triangle APO and triangle ABC
<APO = <ABC [corresponding angles]
<PAO = <BAC [common angle]
triangle APO ~ triangle ABC (by AA)
triangle APO /triangle ABC = (AP/AB)^2 = (2/2+3)^2 = 4/25 (using theorem)

In triangle APO and triangle CQO
<AOP = <COQ [vertically opposite angles]
<APO = <OQC [alternate interior angles]
triangle APO ~ triangle CQO (by AA)
triangle APO/triangle CQO = (AP/CQ)^2
= (AP/PB)^2 = (2/3)^2 = 4/9