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ICSE Question Bank
2024Q7(i)(c)Tangents and Intersecting Chords
NumericalEasy1 mark
7(i)

In the given diagram, an isosceles ∆ABC is inscribed in a circle with centre O. PQ is a tangent to the circle at C. OM is perpendicular to chord AC and ∠COM = 65°. Find :

Figure for this question

∠BCQ

Topic: Tangents / intersecting chords

Previous-year question practice database

Answer

Exam answer

We know that, The angle formed between the tangent and the chord through the point of contact of the tangent is equal to the angle formed by the chord in the alternate segment. ∴ ∠BCQ = ∠BAC = 50°. Hence, ∠BCQ = 50°.

Explanation

Apply the relevant circle theorem to the labelled angles or chords in the figure; the numerical value in the Solution follows from that theorem and the given angles.

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