Question

From an external point P two tangents PA and PB are drawn to the circle with centre O. prove

that OP is the perpendicular bisector of A

Answer 1

we know that the atngent of circle is pependicular to the radius through the point of contact

so
pa perpenducale to oa=angle oap=90 degree
pb perpenducalr ob=angle obp=90 degree
angle oap+angle obp=90+90=180 degree

we know that sum of all angles of quadrelateral is 360

so
angle oap+obp+angle apb +aob=360
from i nd ii we get
angle apb+angle aob =180