A circle with radii marked is inside a triangle.
If △CDE
has sides that are tangent to the circle, and CF=15 cm
, BD=12 cm
, and EG=4 cm
, then what is the perimeter of △CDE
?
(1 point)
cm
The perimeter of a triangle is the sum of the lengths of its sides.
In this case, we are given that CF = 15 cm, BD = 12 cm, and EG = 4 cm. Since CF and BD are tangent to the circle, they are equal in length and can be considered as the segments of the triangle that are on the circle. Let x be the length of each of these segments.
Since the segments are radii of the circle, we can create right triangles within the triangle CDE. Let's extend CF, BD, and EG to intersect at a point O, the center of the circle.
Now we have right triangles COF, BOD, and EOG.
Since CF = BD = x, CO = 15 cm and OD = 12 cm. BC is the sum of the 2 segments on the circle, so BC = 2x.
From the right triangle COF, we have:
x^2 + 15^2 = CO^2
x^2 + 225 = 225
x^2 = 0
x = 0
Now, consider the right triangle BOD. We have:
x^2 + 12^2 = OD^2
x^2 + 144 = 144
x^2 = 0
x = 0
So, the lengths of the 2 segments on the circle are 0, which is not possible. This means there is a mistake in the given information or question setup. Please check and provide the correct information, or clarify the question.