Question

if two tangents are inclined at 60 degree are drawn to a circle of radius 3 cm then find length of each tangent​

Answer 1

Solution :- (from image)

in ∆OAP and ∆OBP, we have,

→ ∠OAP = ∠OBP = 90° (tangents are perpendicular to radius)

→ OP = OP = Hypotenuse (common)

→ OA = OB = radius

so,

→ ∆OAP ~ ∆OBP (By RHS)

then,

→ ∠OPA = ∠OPB (By CPCT)

→ ∠OPA = 60/2 = 30° .

therefore, In right angled ∆OAP ,

→ tan 30° = OA / AP

→ (1/√3) = 3/AP

→ AP = 3√3 cm.

hence,

→ AP = BP = 3√3 cm . (Ans.) { Tangents from same external points to the circle are equal. }

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