To find the length of PG, we can set up an equation using the Pythagorean theorem since a diameter of a circle is twice the radius.
Consider triangle PGF. We have:
(FP)^2 + (PG)^2 = (FG)^2
Since PG is the diameter, FG = 2(PG). So we have:
(FP)^2 + (PG)^2 = (2PG)^2
(FP)^2 + (PG)^2 = 4(PG)^2
Given that FP is x-4 and PG is x, we can substitute these values in:
(x-4)^2 + x^2 = 4x^2
x^2 - 8x + 16 + x^2 = 4x^2
2x^2 - 8x + 16 = 4x^2
2x^2 - 8x + 16 - 4x^2 = 0
-2x^2 - 8x + 16 = 0
Now we need to solve this quadratic equation to find the value of x. The length of PG is then x. Let's use the quadratic formula:
x = (-(-8) ± √((-8)^2 - 4*(-2)*16))/(2*(-2))
x = (8 ± √(64 + 128))/(-4)
x = (8 ± √192)/-4
x = (8 ± 4√3)/-4
x = -2 ± √3
Now x could be either of the roots, but in the context of the problem, length cannot be negative. So the length of PG would be x = -2 + √3. Approximating this gives us around 0.73.
Therefore, the length of PG is approximately 0.73. The closest whole number to this would be 1.
Hence, the correct response is 1.
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.
Circle G as described in the problem. Angle F P G and angle V O K are marked as right angles. If PG=x−4
and GO=12x+3,
what is the length of PG¯¯¯¯¯¯¯¯?
Responses
14
14
10
10
7
7
−1
1 answer
1 answer