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In the figure, TZ is tangent to the circle QPZ. Find x if TZ =...

Mathematics
JAMB 1999

In the figure, TZ is tangent to the circle QPZ. Find x if TZ = 6 units and PQ = 9 units
  • A. 3
  • B. 4
  • C. 5
  • D. 6
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Correct Answer: Option A
Explanation
In \(\bigtriangleup\)WOP, b2 = r2 - (4.502...........(i)

In \(\bigtriangleup\)WOT, b\(\bigtriangleup\) + (4.5 + x)2 = a2...........(ii)

In \(\bigtriangleup\)ZOT, a2 = 62 + r2 ..........(iii)

subst. equation (iii) and (i) in eqn (ii)

r2 - (4.5)2 + (4.5 + x)2 = 36 = 20.25

= (4.5 + x)2 = \(\sqrt{56.25}\) = (4.5 + x)

= 56.25

= 4.5 + x = 7.5

x = 3.0m

x =

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