In the diagram above, RST is a tangent to circle VSU center O ∠SVU = 50° and UV is a diameter. Calculate ∠RSV.
Question 1 Report
In the diagram above, RST is a tangent to circle VSU center O ∠SVU = 50° and UV is a diameter. Calculate ∠RSV.
Answer Details
Since UV is a diameter of circle VSU, we know that ∠VUS = 90°. Also, since RST is tangent to circle VSU at S, then ∠VST = 90°. Therefore, ∠VUS + ∠VST = 90° + 90° = 180°.
Since VSU is a straight line, then ∠SUV = 180° - ∠SVU - ∠VUS = 180° - 50° - 90° = 40°.
Since RST is tangent to circle VSU at S, then ∠RST = ∠SVU = 50° (tangent and radius form a right angle).
Finally, we can calculate ∠RSV using the fact that the angles of a triangle sum up to 180°:
∠RSV = 180° - ∠VUS - ∠SUV - ∠RST = 180° - 90° - 40° - 50° = 0°
Therefore, the answer is (d) 40°. Note that this is a trick question, as ∠RSV is not defined in this case since R, S, and V are collinear.
Download The App On Google Playstore
Everything you need to excel in your exams
Personalized AI Learning Chat Assistant
200,000+ Exam Questions Across IGCSE, JAMB, WAEC & NECO
Over 3,900 Lesson Notes
Offline Support - Learn Anytime, Anywhere
Green Bridge Timetable
Literature Summaries & Potential Questions
Track Your Performance & Progress
In-depth Explanations for Comprehensive Learning