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 :
∠BAC
Topic: Tangents / intersecting chords
Previous-year question practice database
Answer
Exam answer
In △ABC, AB = AC (Given) ACB = ∠ABC = 65° (Opposite angles of equal sides are equal) By angle sum property of triangle, ACB + ∠ABC + ∠BAC = 180° 65° + 65° + ∠BAC = 180° BAC = 180° - 65° - 65° = 50°. Hence, ∠BAC = 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.