Q1. [1] § 10.1 Introduction § 10.2 Tangent to a Circle § 10.4 Summary
In the given figure, AT is tangent to a circle centred at O. If $\angle CAT = 40°$, then $\angle CBA$ is equal to
- (A) $70°$
- (B) $50°$
- (C) $65°$
- (D) $40°$
Previously asked in CBSE board exam
2024 30/2/1 Q17
Generated by claude-sonnet-4-6 · 2026-06-15 10:22 · grounding rag
Model Answer
(B) 50°
By the tangent-chord angle theorem, ∠CAT = ½ × arc CA, so arc CA subtends 80° at centre. ∠CBA (angle in alternate segment) = 90° − 40° = 50°.
Explanation
The angle between a tangent and a chord equals the inscribed angle in the alternate segment (Tangent-Chord angle = Alternate Segment Theorem). Here ∠CBA = 90° − ∠CAT = 90° − 40° = 50°. Examiners expect you to identify and apply the alternate segment theorem directly.
Source: Chapter 10, Circles (Tangent to a Circle / properties)
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