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In the given figure, 0 is the center of a circle, BOA is its diameter and the tangent at the point P meets BA extended at T. If ∠PBO = 30° then ∠PTA = ?
OB = OP [radii of same circle]
∠OPB = ∠PBO
[Angles opposite to equal sides are equal]
As, ∠PBO = 30°
∠OPB = 30°
∠OPT = 90°
[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]
∠BPT = ∠OPB + ∠OPT = 30° + 90° = 120°
Now, In ΔBPT
∠BPT + ∠PBO + ∠PTB = 180°
120° + 30° + ∠PTB = 180°
∠PTB = 30°
∠PTA = ∠PTB = 30°