Question

From an external point P. two tangent PT and PS are drawn to a circle with centre O and radius r. If OP = 2r show that

Answer 1

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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:-
AP is the tangent to the circle.
∴ OA ⊥ AP (Radius is perpendicular to the tangent at the point of contact) 
∠ OAP = 90º
In Δ OAP,
sin ​∠OPA= OA/OP=R/2R =1/2 
∠OPA=30 
In ​Δ 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

hope it helps ✌