GCE Mathematics 2022 Objective — Question 30

Question 30 of 50 from the General Certificate of Education (GCE) Mathematics 2022 Objective paper, with the correct answer and a full explanation.

In the diagram, MNR is a tangent to the circle centre N and angle NOS=108 degrees. Find angle OSN.

• A. 72 degrees
• B. 42 degrees
• C. 36 degreesCorrect
• D. 18 degrees

Explanation

Triangle ONS is isosceles (|ON|=|OS|, radii), so angle OSN = angle ONS = x. Since angle NOS=108, then 108+x+x=180 (angles in a triangle), so 2x=72, x=36 degrees.

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