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If the opposite sides of a, B and C are a, B and C respectively, and Tan C = 43 and C = 8, then the radius of △ ABC circumcircle is () A. 10B. 8C. 6D. 5
∵ Tanc = 43, ∵ COSC = 35, sinc = 45. From the sine theorem, we can get 2R = csinc = 845 = 10, ∵ r = 5, so we choose D
It is known that the diameter of the circumscribed circle of Δ ABC is 1, and ABC is an arithmetic sequence. If the edge opposite the angle ABC is ABC, find a ^ 2 + C ^ 2
It is known that the diameter of the circumscribed circle of Δ ABC is 1, and ∠ a, B and C form an arithmetic sequence. If the opposite sides of ∠ a, B and C are a, B and C respectively, find a ^ 2 + C ^ 2
Because ∠ a, ∠ B, and ∠ C form an arithmetic sequence 〈 2 ∠ B = a + C ------- (1)
The three internal angles of Δ ABC are ∠ a, ∠ B, ∠ C = 180 ° - (2)
Simultaneous equations (1) and (2) can be solved: a = 90 °, B = 60 ° and C = 30 °
The opposite side C of right angle a is the diameter, that is, the opposite side a of ∠ C of C = 1,30 ° is 1 / 2
∴a^2+c^2=(1/2)^2+1^2=5/4
In the triangle ABC, ab = 3, 2A = 30 degrees, circumcircle radius is 2, find AC
BC/sinA=2R,
BC=1/2*2*2=2,
cos30=(3^2+AC^2-2^2)/2*3*AC,
AC^2-3√3*AC+5=0,
(AC-3√3/2)^2=7/4,
AC = (√ 7 + 3 √ 3) / 2, or AC = (3 √ 3 - √ 7) / 2
As shown in the figure, ⊙ o is the circumscribed circle of △ ABC, ∠ B = 60 °, Op ⊥ AC at point P, Op = 23, then the radius of ⊙ o is ()
A. 43B. 63C. 8D. 12
The arc of ∵ center angle ∵ AOC and circumference angle ∵ B is AC, and ∵ B = 60 °, and ∵ AOC = 2 ∵ B = 120 °, OA = OC, ∵ OAC = ∵ OCA = 30 °, and ∵ op ⊥ AC,
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