Question

if a line 1 is the bisector of <A, then find OQ

Answer 1

In triangle AOP and triangle AOQ,
angle OAP=angleOAQ.(AO bisector)
angleOPA=angleOQA.(Each 90 degrees)
AO=AO (Common side)
Therefore,
Triangle AOP is congruent to triangle AOQ.(AAS rule)
Therefore,
AP=AQ (By C.P.C.T)
Also,
QO=OP(By cpct)
Therefore,
AQ=4 cm.
Then apply pythagoras theorum in both triangles you will get answer.hope it helps