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

In the figure, TZ is tangent to the circle QPZ. Find x if TZ = 6 units and PQ = 9 units

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 =