PART A
From the figure,
PQ is a tangent (given)
OP is a radius (given)
Therefore, Triangle QOP is a right-angled triangle
So to calculate side OP, we use the Pythagoras theorem
[tex]\begin{gathered} x^2+24^2=25^2 \\ x^2+576=625 \\ x^2=625-576 \\ x^2=49 \\ x=\sqrt[]{49} \\ x=7 \end{gathered}[/tex]Therefore, OP is equal to 7 units.
PART B
To get line TQ,
TQ = TO + OQ
OQ = 25 (given)
TO = OP (they are both radii of the circle, hence they are the same)
TO = 7
TQ = 7 + 25
TQ = 32
Therefore, TQ is equal to 32 units.
