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In the figure PT is a tangent to the circle with centre at O. If...

Mathematics
JAMB 1983

In the figure PT is a tangent to the circle with centre at O. If PQT = 30o, find the value of PTO

  • A. 30o
  • B. 50o
  • C. 24o
  • D. 12o
  • E. 60o
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Correct Answer: Option A
Explanation

O\(\hat{P}\)T = 90º (The radius is perpendicular to the tangent at the point of contact.)

Sum of angles in \(\triangle\) PQT = 30 + ( 90 + x ) + (x + 2x) = 180

= 120 + 4x = 180

4x = 180 - 120 = 60º

x = \(\frac{60}{4}\) = 15°

Therefore, P\(\hat{T}\)O = 2x = 2 x 15 = 30º

 


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