Question

from an external point P, two tangents PT and PS are drawn to a circle with centre O and radius r. If OP =2r, show that angle OTS=OST=30

Answer 1

AP is the tangent to the circle
OA _|_ AP (Radius is perpendicular to the tangent at the point of contact)
∠OAP = 90 degrees
In angle OAP, 
Sin ∠OPA= OA/OP = R/2R = 1/2
∠OPA = 30
In Angle ABP,
AP = BP
∠PAB = ∠PBA
so 60+ ∠PAB + ∠PBA = 180
60+2 ∠PAB = 180
∠PAB = 180 - 60/2
∠PAB = 60
But
as ∠OAP = OBP = 90
OAP = OBP
so,
60 + x = 90
x = 30
therefore,
∠OTS = OST= 30

Answer 2

Answer:

Step-by-step explanation:below is the CORRECT

answer