What can be said about the relationship between triangles and circles? check all that apply. a) many circles can be inscribed in a given triangle b) exactly one triangle can be inscribed in a given circle c) exactly one circle can be inscribed in a given triangle d) many triangular shapes can be circumscribed about a given circle
I hope this helps~
The triangle – circle relationship has amazing properties, first explored in by Pythagoras. Note how the radius of each circle is exactly twice that of the next smallest circle, and the height of each triangle is 2 times the preceding triangle as well.
The answers are (B) and (D).
Step-by-step explanation: We are given four options describing the relationship between circles and triangles. We are to select the correct statements.
Since a circle has infinitely many non-collinear points, and we need three non-collinear points to draw a triangle, so we can draw many triangular shapes can be inscribed in a given circle.
So, option (A) is incorrect and (B) is correct.
Now, we can draw a circle with centre as the in centre of a triangle and a triangle has only one in centre, so we can inscribe many circles inside a triangle with centre as incentre.
Hence, option (C) is incorrect.
Also, considering the construction symmetry, we can conclude that exactly one circle can be circumscribed about a given triangle. Therefore, option (D) is also correct.
Thus, (B), (C) and (D) are correct.
Following are relation between Circle and Triangle:
1. Both circle and triangles are plane figures.
2. One circle is inscribed in a given triangle which is the largest circle that can be inscribed while Many triangle cane be inscribed in a circle. This circle is called incircle.
3. There also only one circle that passes through all vertices of a triangle. That circle is called circumcircle.
The points are below.
We have to tell about the relationship between triangles and circle.
Several points are:
- Both circle and triangles are lane figures.
- Triangle has 3 vertices. On the other hand circle has infinitely many vertices.
- Exactly one circle can be inscribed in a given triangle but many triangular shapes or triangles can be circumscribed in a given circle.
- Circles and triangles both are geometric shapes or figures, and their areas can be calculated using certain formulas.
you can say that One and only one circumference passes through 3 non-aligned points.
B) many triangular shapes can be inscribed in a given circle; and
D) exactly one circle can be circumscribed about a given triangle.
One of our geometric theorem states that for any 3 non-collinear points, exactly one circle can be drawn through it. This explains answer D; the non-collinear points would be the vertices of the triangle, and only one circle can be drawn through those points (circumscrbied about the triangle).
For B, we can have many triangles inscribed in a circle; the differences in the measures of the angles used will create the different triangles.