True or False
If angle between two tangents drawn from a point P to a circle of radius a and centre O is 60°, then OP = `asqrt(3)`
This statement is True.
From point P, two tangents are drawn
Given, OT = a
Also, line OP bisects the ∠RPT.
∴ ∠TPO = ∠RPO = 30°
Also, OT ⊥ PT
In right-angled ΔOTP,
`sin 30^circ = (OT)/(OP)`
⇒ `1/2 = a/(OP)`
⇒ OP = 2a
Concept: Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
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