Question

two tangents pa and pb are drawn to the circle o, such that apb =120 degree.prove that op = 2ap

Answer 1

apo=60°
cos 60°=ap/op
1/2=ap/op
2ap=op

Answer 2

! Given: "o"is centre

! PA &PB are tangent

<APB=120....

Proof: In the fig.. tri<..OAP&OBP

! OP=OP...(common)

! <OAP=<OBP... all 90®

! both triangle is congurent

! ........by the RHS criterion

! cos 60=AP

! OB

! 1=AP

! 2=OB

! ·: 1*OB=2*AP

! ·: IT can proved that AP=2OB