Chapter 6 exercises

1 (UnB-Adapted)

Check which of the following items are true:

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A
In a general triangle, the circumscribed and inscribed circumferences are necessarily concentric.
B
If r is the radius of the inscribed circumference and the triangle is equilateral, then the side is .
C
The vertices of the triangle are equidistant from the center of the inscribed circumference.
D
If the triangle inscribed on the circumference with a radius of 2 cm has a right angle, then one of the sides measures 4 cm.

2 (ENEM -adapted)

A metallurgical company received an order to manufacture, in large quantities, a piece with the shape of a straight prism with a triangular base, whose base dimensions are 6 cm, 8 cm and 10 cm. This shape must be cast in such a way that the perforation, in the form of a straight circular cylinder, is tangent to the lateral faces, as shown in the figure. The perforation radius of the piece is (note that 6, 8 and 10 is a Pythagorean triple)

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3 (Dolce & Pompeu-adapted) Check the following items that are true.

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A
The incenter is the center of the inscribed circumference in the triangle.
B
The circumcenter is the center of the circumscribed circumference of the triangle.
C
The incenter is internal to the triangle.
D
The barycenter is internal to the triangle.
E
The orthocenter is internal to the triangle.
F
The circumcenter is internal to the triangle.
G
The barycenter is the center of the circumscribed circumference of the triangle.

Verifique minha resposta (3)

The following figure represents an triangle ABC with an inscribed circumference. Knowing that the sides AB, BC and AC are 7, 5 and 6, respectively, calculate the measure of the segment EC.

5) Consider the following statements:

The diagonals of the parallelogram intersect at the midpoint.

The three medians of a triangle intersect at the same point that divides each median into two parts, so that the part containing the vertex is twice the length of the other one.

Based on this information and your previous knowledge, solve the following problem: Determine the value of x, knowing that the quadrilateral ABCD is a parallelogram and M is the midpoint of AB.

6 (Dolce & Pompeu) - Since H is the orthocenter of a triangle ABC and BC=150º, determine .

7 (Dolce & Pompeu) - If P is the incenter of a triangle ABC and BC=125º, determine .

8 (Dolce & Pompeu) -The circumference of an isosceles triangle is internal to the triangle and two perpendicular bisectors form an angle of 50º. Determine the angles of this triangle.

Chapter 6 exercises

1 (UnB-Adapted)

2 (ENEM -adapted)

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