Question

Show visually how you worked out the problem all the way please

Answer 1

Solution:

Given:

A triangle PMT

The triangle shows the steps in the construction of inscribing a circle in a triangle.

To inscribe a circle, the common centre G is the centre of the circle to be inscribed.

If G is the centre, then;

$KG=GH=GJ\ldots\ldots.\ldots\ldots.\ldots(\text{radi}i\text{ of the circle)}$$\begin{gathered} \text{Where;} \\ GH=x+3 \\ GJ=2x-1 \end{gathered}$

Substituting and equating the equations;

$\begin{gathered} GH=GJ \\ x+3=2x-1 \\ \text{Collecting the like terms,} \\ 3+1=2x-x \\ 4=x \\ x=4 \end{gathered}$

The measure of segment PG will thus be,

$\begin{gathered} PG=4x+1 \\ \text{Substituting the value of x,} \\ PG=4(4)+1 \\ PG=16+1 \\ PG=17\text{units} \end{gathered}$

Therefore, the measure of segment PG is 17 units.

The correct answer is option D.