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JAMB Mathematics 1993 Question 34

Question 34

Circle Theorems

In the figure above, the line segment ST is tangent to the two circle at S and T, O and Q are the centres of the circles with OS = 5cm, QT = 2cm and OQ = 14cm. Find ST.

Diagram for this question
  1. A.7√3cm
  2. B.12cm
  3. C.√87cm
  4. D.7cm
Show the answer and explanation

Answer: A (7√3cm)

Explanation

The tangent crosses the line of centres, so make a right triangle with hypotenuse OQ = 14 and one side 5 + 2 = 7. Then ST = √(196 − 49) = √147 = 7√3cm.