TP and TQ are the tangents from the external point T of a circle with centre O. If ∠ OPQ = 30° then find the measure of ∠ TQP.
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TP & TQ are the two tangents drawn from the external point P of a circle with Centre O.
∠ OPQ = 30°
In the figure Join OP, OQ & PQ
∠ OPT = ∠ OQT = 90°
[We know that the tangent at any point of a circle is perpendicular to the radius through the point of contact.]
In ∆OPQ,
OP = OQ [ radius of the circle]
∠OPQ = ∠OQP = 30°
[Angles opposite to equal sides of a ∆ are equal]
∠TQP = ∠OQT - ∠OQP
∠TQP = 90° - 30°
∠TQP = 60°
Hence, the the measure of ∠TQP is 60°.
HOPE THIS WILL HELP YOU..
TP & TQ are the two tangents drawn from the external point P of a circle with Centre O.
∠ OPQ = 30°
In the figure Join OP, OQ & PQ
∠ OPT = ∠ OQT = 90°
[We know that the tangent at any point of a circle is perpendicular to the radius through the point of contact.]
In ∆OPQ,
OP = OQ [ radius of the circle]
∠OPQ = ∠OQP = 30°
[Angles opposite to equal sides of a ∆ are equal]
∠TQP = ∠OQT - ∠OQP
∠TQP = 90° - 30°
∠TQP = 60°
Hence, the the measure of ∠TQP is 60°.
HOPE THIS WILL HELP YOU..
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Answer:
L TQP = 60°
Step-by-step explanation:
For explanation see the attachment....
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