In the figure, TZ is tangent to the circle QPZ. Find x if TZ = 6 units and PQ = 9 units
Attached Figure / Diagram
A
3
B
4
C
5
D
6
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
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 =
Source: Myschool Past Questions Archive (Record #33087)