The circumference of a right triangle is 6 + 2 3. The center line on the hypotenuse is 2. Find the area of the right triangle______ .

∵ ACB = 90 °, CD is the center line on the bevel, CD = 2,
∴AB=2CD=4，
∵AB+AC+BC=6+2
3，
∴AC+BC=2+2
3，
According to Pythagorean theorem, ac2 + BC2 = AB2 = 16,
(AC + BC) 2-2ac · BC = 16, i.e. 8
3-2AC•BC=0，
∴AC•BC=4
3，
The area of this right triangle is: 1
2AC•BC=2
3．
So the answer is: 2
3．

Another question: the perimeter of a right triangle is (2 + root 6) cm, and the central line on the hypotenuse is 1cm. What is the area

According to the Pythagorean theorem, a ^ 2 + (root 6-A) ^ 2 = 2 ^ 2A ^ 2 + A ^ 2-2

As shown in Fig. 9, in RT △ ABC, CD is the height on the edge of the hypotenuse AB, AC = 20, BC = 15. Try to find the values of Tan ∠ BCD and Tan ∠ ACD

∵ RT △ ABC, ∵ ACD = 90 °, AC = 20, BC = 15
∵CD⊥AB
∴∠A+∠ACD=90°,∠B+∠BCD=90°
∵∠A+∠B=90°
∴∠ACD=∠B,∠BCD=∠A
∴tan∠BCD=tan∠A=BC/AC=15/20=¾
tan∠ACD=tan∠B=AC/BC=20/15=4/3

As shown in the figure, in △ ABC, ∠ ACB = 90 °, BC = 6, AC = 8, CD ⊥ AB, find the value of sin ∠ ACD and the value of Tan ∠ BCD chart

According to Pythagorean theorem, ab = 10 can be obtained
sin∠ACD=sin∠B=AC/AB=8/10=4/5
tan∠BCD=tan∠A=BC/AC=6/8=3/4
According to: if two angles are equal, their corresponding trigonometric function values are equal

As shown in the figure, in △ ABC, ∠ ACB = 90 °, BC = 3, AC = 4, CD ⊥ AB, the perpendicular foot is D, and Tan ∠ BCD and Tan ∠ ACD are calculated

From BC = 3, AC = 4, according to Pythagorean theorem, ab = 5
From CD ⊥ AB, we can see that,
tan∠ACD=tan(90°-∠A)=tan∠B=4/3
tan∠BCD=tan（90°-∠B）=tan∠A=3/4

In △ ABC, ∠ ACB = 90 °, BC = 3, AC = 4, CD ⊥ AB, the perpendicular foot is D, and the values of sin ∠ ACD and Tan ∠ BCD are obtained

From BC = 3, AC = 4, according to Pythagorean theorem, ab = 5
From CD ⊥ AB, we can see that,
sin∠ACD=sin(90°-∠A)=sin∠B=3/5
tan∠BCD=tan（90°-∠B）=tan∠A=3/4

In RT △ ABC, ∠ C = 90 °, AC = 6, BC = 8, then the radius of inscribed circle of △ ABC is r = () A. 1 B. 2 C. 3 D. 5

As shown in the figure, ⊙ o cuts AC to e, cuts BC to F, cuts AB to g, connects OE, of, ⊥ AC, of ⊥ BC, ⊥ quadrilateral CEOF is a square, ∵ C = 90 °, AC = 6, BC = 8, ⊙ AB = 10. If the radius of ⊙ o is r, then CE = CF = R,  AE = Ag = 6-r, BF = BG = 8-r, ᚉ AB = Ag + BG = AE + BF, that is, 6-r + 8-r = 10

In RT △ ABC, ∠ C = 90 °, AC = 6, BC = 8, then the radius of inscribed circle of △ ABC is r = () A. 1 B. 2 C. 3 D. 5

As shown in the figure, ⊙ o cuts AC to e, BC to F, AB to g, and OE, of,
∴OE⊥AC，OF⊥BC，
The quadrilateral CEOF is a square,
∵∠C=90°，AC=6，BC=8，
∴AB=10，
Let the radius of ⊙ o be r, then CE = CF = R,
∴AE=AG=6-r，BF=BG=8-r，
ν AB = Ag + BG = AE + BF, that is, 6-r + 8-r = 10,
∴r=2．
Therefore, B

In RT △ ABC, ∠ C = 90 °, AC = 6, BC = 8, then the radius of inscribed circle of △ ABC is r = () A. 1 B. 2 C. 3 D. 5

In the right triangle ABC, the angle c = 90 °, AC = 3, BC = 4. The circle with point C as the center and Ca as the radius intersects AB and BC respectively In the right triangle ABC, the angle c = 90 °, AC = 3, BC = 4. The circle with point C as the center and Ca as the radius intersects with point d respectively. The length of AB and ad is calculated?

First of all, according to Pythagorean theorem, ab = 5, do ab high CO and ab intersection with O, area method, CO = 12 / 5
Because CD = Ca (radius of circle), and CO is perpendicular to AB, CO is also the median line of AD, that is, O is the midpoint of AD. according to the Pythagorean theorem, Ao = 9 / 5, ad = 18 / 5

The circumference of a right triangle is 6 + 2 3. The center line on the hypotenuse is 2. Find the area of the right triangle______ .