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Given that the circle O is the circumscribed circle of triangle ABC, and the side length is 6, the radius of circle O is calculated
If the side length is 6, then the height of an equilateral triangle is equal to 3 root sign 3. The intersection of the three midlines is the center of the circumscribed circle, and its distance from the vertex of each triangle is equal to two-thirds of the length of the midline
So, multiply 3 by 2 / 3 to get 2 root sign 3. So the radius of this circle is equal to 2 root sign 3
If the three sides of a triangle are 6 8 10, the radius of its circumcircle is
From 6 ^ 2 + 8 ^ 2 = 10 ^ 2, it can be determined that the triangle ABC is a right triangle
The diameter of the circle is the hypotenuse of the right triangle ABC, equal to 10
That is, the diameter of the circumcircle of the triangle is 10
The radius of circumcircle is 5
See who is smart: in the right triangle ABC, if the hypotenuse AB is 2 and the inscribed circle radius is r, then the maximum value of R is?
When the triangle is an equilateral triangle, the radius of the inscribed circle is r, which is the maximum. When the two radii of the circle are perpendicular to the two right angles, a square is formed, and half of the right angle is equal to R, so r = the root of 2
RELATED INFORMATIONS
- 1. If the hypotenuse BC of the right triangle ABC is 1 and the circle O is the inscribed circle of the triangle ABC, then the maximum radius of the circle O is 0
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- 3. The first side of a triangle becomes {2a-b} cm, the second side is {a = 2B} cm longer than the first side, and the third side is less than 2 times of the first side by B. calculate the perimeter
- 4. Given that the perimeter of the triangle is 5a-b, the length of the first side is 3A + 2B, and the length of the second side is twice that of the first side, which is a-2b + 2 less than that of the first side, the length of the third side can be obtained
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- 6. Xiaosheng drew four points on the paper. If the four points were connected to form a figure, how many triangles would there be in the figure? Please draw a picture to explain
- 7. Fill 10, 15, 20, 30, 40 and 60 in the circle below to make the product of three numbers on each side of the triangle equal
- 8. As shown in the figure, the upper bottom of a trapezoid is 5cm, and the lower bottom is 8cm. The height of a triangle is 4cm. Divide the triangle into two parts with equal area, a and B, and calculate the area of the shadow part
- 9. It is known that a, B and C are the three sides of the triangle ABC, and the positive and negative values of the square of (A-C) - B are judged
- 10. If the lengths of three sides of a triangle are three continuous natural numbers, and its perimeter m satisfies 10 < m < 22, then the triangle has () A. 2 b. 3 C. 4 d. 5
- 11. If the inner and outer centers of a triangle coincide, then the triangle is, and the ratio of the radius of its circumscribed circle to the radius of its inscribed circle is
- 12. If the lengths of the two right sides of a right triangle are 3 and 4 respectively, what is the radius of its inscribed circle
- 13. As shown in the figure, in △ ABC, the bisector of ∠ ABC and ∠ ACB intersects at point I. according to the following conditions, calculate the degree of ∠ BIC 1. If ∠ ABC = 60 °, ACB = 70 °, then ∠ BIC=____ 2. If ∠ ABC + ∠ ACB = 130 °, then ∠ BIC=____ 3. If ∠ a = 50 °, then BIC=____ 4. From the above calculation, what is the quantitative relationship between ∠ A and ∠ BIC? Please prove it
- 14. In the triangle ABC, BD and CE are the midlines on the sides AC and ab. BD and CE intersect at the point O. what is the relationship between the length of Bo and OD? For detailed explanation, do not run to copy, correct answer, I can add 20-50 points to see the picture
- 15. As shown in the figure, in △ ABC, ab = AC, D is a point on the edge of BC, with AB and BD as adjacent sides, make parallelogram ABDE and connect AD and EC
- 16. As shown in the figure, in the triangle ABC, D, e and F are the midpoint of three sides BC, AC and ab respectively. It is proved that the quadrilateral defb is a parallelogram
- 17. (1 / 2) we know that the two high BD and CE of the acute triangle ABC intersect at O, and ob = OC, and prove that: (1) the triangle ABC is isosceles triangle (1 / 2) it is known that the two high BD and CE of the acute triangle ABC intersect at the point O, and ob = OC. It is proved that: (1) the triangle ABC is an isosceles triangle. (2) whether o is at the angular plane of the angle ABC is determined
- 18. What is the area of a right triangle when the length of two right sides of a right triangle is two prime numbers and the sum is 18?
- 19. In an isosceles triangle with a circumference of 10 cm, the length of the bottom edge is x (CM), and the length of the waist is y (CM). Write out the analytic expression of the function of Y with respect to X and the definition domain of the function
- 20. In the triangle ABC, ab = AC, BD is the center line on the side of AC. BD divides the circumference of ABC into two parts: 36 and 63, and calculates the length of BC Let the waist length of this isosceles triangle be a and the bottom length be B be A+A/2=36 B+A/2=63 A = 24, B = 51 is obviously not true Or a + A / 2 = 63 B + A / 2 = 36 A=42 B=15 establish So BC = 15 Why is BD not included in the weekly schedule