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# In the Given Figure, O is the Centre of the Circle. Tangents at a and B Meet at C. If ∠Aco = 30°, Find: ∠Bco - Mathematics

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#### Question

In the given figure, O is the centre of the circle. Tangents at A and B meet at C. If ∠ACO = 30°, find: ∠BCO

#### Solution

In the given fig, O is the centre of the circle and CA and CB are the tangents to the circle from
C. Also, ∠ACO = 30°
P is any point on the circle. P and PB are joined.
To find:  ∠ BCO
Proof:
In ΔOAC and OBC
OC = OC (Common)
OA = OB (radius of the circle)
CA = CB (tangents to the circle)
∴  ΔOAC ≅  ΔOBC (SSS congruence criterion)
∴ ∠ACO =  ∠BCO = 30°

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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 (C) | Q: 20.1 | Page no. 286

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In the Given Figure, O is the Centre of the Circle. Tangents at a and B Meet at C. If ∠Aco = 30°, Find: ∠Bco 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.