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In the Following Figure, Pq and Pr Are Tangents to the Circle, with Centre O. If ∠Qpr = 60°, Calculate: ∠ Qor - Mathematics

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Question

In the following figure, PQ and PR are tangents to the circle, with centre O. If `∠`QPR = 60°, calculate:

∠QOR  

Solution

Join QR.

In quadrilateral ORPQ,
OQ  ⊥ OP,OR ⊥  RP
∴ `∠`OQP = 90°  ,`∠`ORP = 90° ,`∠`QPR = 60°
`∠`QOR 360° -( 90° + 90° + 60°)
`∠`QOR = 360° - 240°
`∠`QOR = 120°

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APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 18: Tangents and Intersecting Chords
Exercise 18 (A) | Q: 18.1 | Page no. 275
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In the Following Figure, Pq and Pr Are Tangents to the Circle, with Centre O. If ∠Qpr = 60°, Calculate: ∠ Qor Concept: Tangent Properties - If a Line Touches a Circle and from the Point of Contact, a Chord is Drawn, the Angles Between the Tangent and the Chord Are Respectively Equal to the Angles in the Corresponding Alternate Segments.
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