Answered

IDNStudy.com, ang iyong mapagkukunan para sa mga sagot ng eksperto at komunidad. Alamin ang mga maaasahang sagot sa iyong mga tanong mula sa aming malawak na kaalaman sa mga eksperto.

In the figure, circle O is inscribed in equilateral triangle ABC and X , Y and Z are the points of tangency. If the side of triangle ABC is 12, how long is the radius of circle O. 

full solutions please and thank you :)

In The Figure Circle O Is Inscribed In Equilateral Triangle ABC And X Y And Z Are The Points Of Tangency If The Side Of Triangle ABC Is 12 How Long Is The Radiu class=

Sagot :

VilesXidn
Given:
side = 12

see figure:

a right triangle is formed.

where the hypotenuse is. h - r
and the other sides are r and 12/2

[tex]h= \sqrt{6^2+12^2} [/tex]

h=10.39

to get the radius we use the Pythagorean theorem.

[tex]10.39-r= \sqrt{(r)^2+(6)^2} [/tex]

[tex]r=3.46[/tex]
View image VilesX
AnneCidn
r = 2 √3

See attached for solution. :)
Btw, I used trig functions, because it is the easiest way to solve it. Haha. I hope you're familiar with that.


<XBO is 1/2 of <XBA. That is why it's 30º
View image AnneC
Salamat sa iyong aktibong pakikilahok. Patuloy na magbahagi ng impormasyon at kasagutan. Sama-sama tayong lumikha ng isang masiglang komunidad ng pagkatuto. Bawat tanong ay may sagot sa IDNStudy.com. Salamat at sa muling pagkikita para sa mas maraming solusyon.