Question

4 ListenExamine the diagram of circle G, where two chords, EF and WV , are congruent.Segment JK is a diameter of circle G and intersects EF at a right angle at point P.JK intersects WV at a right angle at point O.

Answer 1

Given the conditions listed, we know that PG = GO.

Then, we can write:

$\begin{gathered} PG=GO \\ 2(4x-3)-8=4+2x \end{gathered}$

Now we can solve for x as:

$\begin{gathered} 2(4x-3)-8=4+2x \\ 2\cdot4x-2\cdot3-8=4+2x \\ 8x-6-8=4+2x \\ 8x-2x=4+6+8 \\ 6x=18 \\ x=\frac{18}{6} \\ x=3 \end{gathered}$

Answer: x = 3