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In the diagram, the tangent MN makes an angle of 55o with the chord PS....

Mathematics
WAEC 2010

In the diagram, the tangent MN makes an angle of 55o with the chord PS. IF O is the centre of the circle, find < RPS
  • A. 55o
  • B. 45o
  • C. 35o
  • D. 25o
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Correct Answer: Option C
Explanation
Join SR

< PRS = 90o(Angle in a semicircle)

< PRS = 55o (Angle between a chord and a tangent = Angle in the alternate segment)

< PSR + < PRS + < RSP = 180o

90v + 55o + < RSp = 180o

< RSP = 180o - 145o

= 35o

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