Question

I need help on this question

Answer 1

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

`\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}`

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.