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 :
∠ABC
Topic: Tangents / intersecting chords
Previous-year question practice database
Answer
Exam answer
From the figure: ∠AOC = ∠AOM + ∠MOC = 65° + 65° = 130°.
∠AOC is the angle at the centre subtended by arc AC. ∠ABC is the angle at the circumference subtended by the same arc AC.
∠AOC = 2∠ABC 130° = 2∠ABC ∠ABC = 65°.
Answer: ∠ABC = 65°.
Explanation
∠AOC is the central angle and ∠ABC is the angle at the circumference standing on the same arc AC.