a. B and C are the three sides of triangle ABC. It is proved that a ^ 2 = B (B + C) is a = 2B Please give the proof of sufficiency and necessity

Do the angle bisector in B, use the angle bisector theorem, find out the length of CD, DAC is similar to ABC, list the proportion formula, and deduce it

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1. As shown in the figure, ABC is an equilateral triangle, BD is the middle line, extend BC to e, so that CE = CD
2. In known triangle ABC, angle ACB is equal to 90 degrees, AC is equal to BC, ad is vertical to CE, be is vertical to CE, D and E are perpendicular feet
3. Known: as shown in the figure, in △ ABC, if ∠ A is an acute angle, points D and E are on AB and AC respectively, and ∠ DCB = ∠ EBC = 12 ∠ A. verification: BD = CE
4. In the triangle ABC, the points D and E are on AB and AC, and the angle EBC = angle DCB = I / 2 angle a, BD = CE is proved
5. Known: as shown in the figure, in △ ABC, if ∠ A is an acute angle, points D and E are on AB and AC respectively, and ∠ DCB = ∠ EBC = 12 ∠ A. verification: BD = CE
6. Known: as shown in the figure, in △ ABC, if ∠ A is an acute angle, points D and E are on AB and AC respectively, and ∠ DCB = ∠ EBC = 12 ∠ A. verification: BD = CE
7. In △ ABC, the points o and E are on AB and AC respectively, ∠ DCB = ∠ EBC = 1,2 ∠ a, be and CD intersect at point O to prove BD = CE The following first answer is not for junior high school students, the second answer is wrong, also can't be used, hope someone continue to give guidance.
8. In △ ABC, if sin B = 2sinacosc and the cosine of the minimum angle is 3 / 4, (1) judge the shape of triangle ABC, (2) find the maximum angle of ABC
9. In △ ABC, if Sina: SINB: sinc = 2:3:4, then the cosine value of the largest angle=______ ．
10. Finding cosine C in triangle ABC with a = 3, B = 5 and C = 7
11. It is known that a, B and C are the three sides of triangle ABC, and the square of a + the square of 2B + the square of C is equal to 2B (a + C) It is known that a, B and C are the three sides of triangle ABC, and the square of a + the square of 2B + the square of C is equal to 2B (a + C). Try to judge the shape of triangle ABC and explain the reason
12. Let a, B, C be the three sides of triangle ABC, and (C-B) x2 + 2 (B-A) x + A-B = 0, with two equal real roots, prove that triangle ABC is isosceles triangle
13. Factorization of A2 + B2 + c2-2c-2ab-1 Factorization a ^ 2 + B ^ 2 + C ^ 2-2c-2ab + 1,
14. Given A2 + B2 = C2 + D2 = 1, find the value of (AC BD) 2 + (AD + BC) 2 Please write the process in detail, I wait online, please hurry up! Thank you!
15. What is the volume of the cuboid when the area of the three faces passing through the same vertex of the cuboid is 2, 4 and 8 There should be formula and written narration. Thank you
16. Put two cuboids that are 8 cm long, 6 cm long and 5 cm high together to form a large cuboid. How many square centimeters is the maximum surface area of this large cuboid?
17. The cuboid is 12 cm long and 8 cm high. The sum of the areas of the two sides of the shadow is 180 square cm. What is the cuboid's volume in cubic cm
18. The area of three sides of a cuboid is 6, 8 and 12 respectively. What is the volume of this cuboid?
19. The length, width and height of a cuboid are a, B and C meters respectively. If the height increases by 2 meters, and the length and width remain unchanged, the volume of the new cuboid will increase () A. A×B×（C+2）B. 2ABC. 2ABC
20. A five digit 3ab98 can be divided by 99 to find the five digit I really don't understand,