As shown in the figure, △ ABC is inscribed on the circle O, ab = AC, cos ∠ ABC = four fifths. If the radius of circle O is 5cm, calculate the area of △ ABC (2) If BD bisector angle ABC, ah ⊥ CD is in H, find HC: BD

As shown in the figure, △ ABC is inscribed on the circle O, ab = AC, cos ∠ ABC = four fifths. If the radius of circle O is 5cm, calculate the area of △ ABC (2) If BD bisector angle ABC, ah ⊥ CD is in H, find HC: BD

(1) By proving that the triangle ABO is equal to the triangle ACO (SSS), we can prove that the triangle ABM is a right triangle (SAS). We can also prove that the triangle ABN is similar to a triangle ABM.COS Angle ABC = cos angle anb. The length of AB can be obtained, and then the area of triangle ABC is 86.4cm ^ 2
As for the second question, I don't know where D is, so I can't give the answer

In △ ABC, if the angle c = 90 degrees, AC = 12cm, BC = 5cm, then its circumcircle radius R=____ , inscribed circle radius r=_____ (online, etc.)

Using Pythagorean theorem 12 ^ 2 + 5 ^ 2 = 13 ^ 2
Because the diameter is right angle to the center of the circle, r = 6.5
As for the inscribed circle, you can calculate the area of the triangle = 30, then multiply it by 2 and divide it by the sum of the lengths of the sides to get 2

Given that AC = 3cm, BC = 4cm, ab = 5cm in △ ABC, then the circumscribed circle radius of △ ABC is ()
A. 2cmB. 2.5cmC. 3cmD. 4cm

∵ 32 + 42 = 52, ∵ ABC is a right triangle, AB is a hypotenuse, the radius of the circumcircle of the triangle is 12 × 5 = 2.5cm, and the radius of the circumcircle of the triangle is equal to 2.5cm

In the triangle ABC, AC = BC = 5, angle ACB = 120 degrees, find the circumcircle radius of the triangle ABC

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