The area of the inscribed triangle of radius 1 is 0.25. Find the product of the three sides of the triangle

The area of the inscribed triangle of radius 1 is 0.25. Find the product of the three sides of the triangle

The product of the three sides of this triangle is not a fixed value

If the radius of a circle is 1 / 4, then the product of the two sides ABC =? Please write more details, thank you!

S=1/2absinC=(1/2)ab*c/2r=abc/4r
=>abc=1

In the triangle ABC, the angle BAC is equal to 90 degrees. Take AB as the diameter to make the circle O intersect BC at point E, and cross e as the tangent of circle O intersect AC at D, which proves that ad = CD

O is the midpoint of AB, so QAD = 90 degrees, De is tangent to circle O, so OE is vertical De, so OED = 90 degrees, then the common side OD, OE = OA, in the right triangle OAD and right triangle OED, so ad = de;
In addition, de = DC
So ad = DC

A B C is inscribed in the circle O, ad is the diameter of the circle O, e is a point on the extension line of CB and ∠ BAE = ∠ C. It is proved that the straight line AE is the tangent of circle o

Connect CD
∵ ad is the diameter of the circle
∴∠ACD=90°
∵ BCD = ∵ bad (equal to the circular angle on the arc)
∠ACB=∠BAE
∴∠BAE+∠BAD=∠ACB+∠BCD=∠ACD=90°
That is, ∠ ead = 90 °
∴OA⊥AE
/ / AE is the tangent of circle o

Additional question: as shown in the figure, it is known that △ ABC is inscribed in ⊙ o, AB is the diameter, ∠ CAE = ∠ B Verification: AE and ⊙ o are tangent to point a

It is proved that: ∵ AB is the diameter,
∴∠ACB=90°，
∴∠BAC+∠B=90°，
And ∵ CAE = ∵ B,
∴∠BAC+∠CAE=90°，
In other words, BAE = 90 °,
So AE and ⊙ o are tangent to point a

As shown in the figure, AE is the tangent of ⊙ o, the tangent point is a, BC ∥ AE, BD bisection ∠ ABC intersects AE at point D and AC at point F (1) Confirmation: AC = ad; (2) If BC= 3，FC=3 2. Find AB length

(1) It is proved that: make the diameter Ag cross BC to h, ∵ AE is the tangent line of ⊙ o, the tangent point is a, ∵ Ag ⊥ ad, ∵ BC ∵ AE, ? Ag ⊥ BC, ? AG is the diameter, ? AG is the vertical bisector of BC, ? AB = AC, ∵ BD bisection ? ABC, ? abd = ∠ a

As shown in the figure, ad, AE, CB are tangent lines of ⊙ o, D, e, f are tangent points respectively, ad = 8, then the circumference of ⊙ ABC is () A. 8 B. 10 C. 12 D. 16

∵ ad, AE and CB are tangent lines of ⊙ o, and D, e and F are tangent points respectively,
∴CE=CF，BD=BF，AE=AD=8，
The circumference of △ ABC is: AC + BC + AB = AC + CF + BF + AB = AC + CE + BD + AB = AE + ad = 16
Therefore, D

The triangle ABC is inscribed in the circle O, the point D is on the extension line of OC, SINB = 1 / 2, angle cab = 30 °. It is proved that ad is the tangent line of circle o

(1) Since SINB = 1 / 2, angle B = 30 °, then angle AOC = 60 °, angle CAD = angle B = 30 °
And OA = OC, so the triangle OAC is equilateral triangle, and the angle OAC = 60 °
Then the angle oad = 60 ° + 30 ° = 90 °, so ad is tangent to circle o
(2) From od vertical AB, BC = 5, so OA = OC = 5
Ad = oatan 60 ° = 5 times root number 3

1) prove that ad is tangent of circle O; 2) if OD ⊥ AB, BC = 5, calculate ad length

Connect OA
∵∠ABC=30°
∴∠AOC=60°
∵OA=OC
The △ AOC is an equilateral triangle
∴∠OAC=60°
∵∠CAD=30°
∴∠OAD=90°
/ / AD is the tangent of circle o
2) AB crosses od at point E
BC=5
∴OE=CE=2.5
∴AO=5
/ / ad = 5 root number 3

As shown in the figure, it is known that △ ABC is inscribed in the circle O, the point D is on the extension line of OC, SINB = 1 / 2, ∠ d = 30 degrees, and it is proved that ad is a circle As shown in the figure, it is known that △ ABC is inscribed in the circle O, the point D is on the extension line of OC, SINB = 1 / 2, ∠ d = 30 degrees Prove that ad is tangent of circle O (2) if AC = 6, find the length of AD Using junior high school knowledge to solve emergency

First of all, if angle B = 30 degrees, then angle AOD = 60 degrees, and angle d = 30 degrees, so angle oad = 90 degrees, Ao is radius, so ad is tangent line of circle o
AOC is an equilateral triangle and AO = AC = 6
In the AOD of a right triangle, the angle AOD = 60 degrees, resulting in AD = 6 root sign 3