Question

PA and PB are tangents to the circle with centre O touching it at A

and B respectively. If ∠APO = 30 then ∠POB ____​

Answer 1

step by step explanation.

PA = PB ( two tangents from a point are equal.)

OP = OP ( common)

angle PAO = angle PBO. ( 90 degree each.)

there triangle are congruent by R.H.S

therefore angle POB = POA

angle PAO + angle APO + angle POA = 180 degree. ( angle sum property of triangle.)

90 + 30 + POA = 180.

120 + POA = 180.

angle POA = 180 -120.

angle POA = 60.

as we prove above angle POA = angle POB

therefore angle POB = 60 degrees