📚 CBSE Grade-10 Study Guide Open in the Study Guide single page app →
HomeMathematics

Mathematics — CBSE Class 10 board question

Q1. [1]
In the given figure, AT is tangent to a circle centred at O. If $\angle CAT = 40°$, then $\angle CBA$ is equal to
  1. (A) $70°$
  2. (B) $50°$
  3. (C) $65°$
  4. (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)

If a question refers to an image, map, graph or diagram that is not shown here, open the Study Guide single page app, go to Library and find the actual CBSE question paper. The original papers are also available on the CBSE website: cbse.gov.in.
Previous-year CBSE Grade 10 board exam questions, organised by subject and chapter, each with a model answer — free to read and print.