Can you find the Radius of the circle? | (Triangle inscribed in a circle) | #math #maths

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Can you find the Radius of the circle? | (Triangle inscribed in a circle) | #math #maths

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[wackojacko]

Area of triangle can be found using Heron's Formula. Then (13 × 15 × 14) ÷ (4 × Area) = R. 🙂

[michaelpantano]

Pick any angle in the trianle to be theta. Lets say oppose of 15.
Law of cosine:
Cos(theta) = (13^2 + 14^2 - 15^2) / (2*13*14) = 5/13
Sin^2 + cos^2 = 1, so sin(theta) = 12/13
(You can note here we are getting the 5, 12, 13 triangle you had)
Extended law of sines says
2R = a/sin, so 2R = 15/sin(theta)
R = 1/2 * 15/(12/13) = (13*15) / (2*12) = 65/8

[samsheerparambil]

By combining sine law and area of triangle we can say R=abc/4*Area hope this helps.

Area= square root of s(s-a)(s-b)(s-c)

[riccardobaiocco]

Very clear. You are a very good teacher

[rangaswamyks]

GREAT WORK PROFESSOR.. YOU ARE MY FAVOURITE MATHS GURUJEE
AFTER A LONG TIME IAM WATCHING YOUR VIDEOS.. BLESS ME SIR.

[michaelstahl]

I enjoyed your video. My suggestion is using the cosinus theorem for calculating angel alpha at point A . I got alpha nearly 67, 3 . After that I used a theorem for calculating the radius of the circle
around the triangle . r = a / 2 * sin (alpha) = 15 / 2 * 0, 92 = 8, 125.

[suyogbakliwal]

We know that

🔼 = abc / 4R, Where 🔼 is the Area of Triangle ABC, a, b, c are the sides of the triangle, and R is the circumradius of the circle.
The area of a triangle can be found using Heron's formula. and we can find R consequently

[dickroadnight]

Think outside the triangle!
The sides of a circumscribed circle are chords of that circle and the perpendicular chord bisecting lines pass through the centre O of the circle.
The lines from the corners to the centre of the circle are radii. Make D the midpoint of AB, and E the midpoint of AC.
Extend EO to F on AB extended.
By the cos rule A = 67.18 degrees.
The radius is AO = r.
AEF is a right angle triangle.
AE = AC/2 = 6.5
AD = AB/2 = 7
AF = AE/cosA = 16.9
DF = AF-AD = 9.9
AFE = A-90 degrees
OD = DF tan(90-A) = 4.125
r^2 = AD^2 + OD^2 By Pythagoras’ therom
Radius = 8.125

[marcelowanderleycorreia]

Many diferent forms to do. I used the heron formula in order to find the area of the triangle ABC and the proporcionaly of the chords in a circle, in order to find the radus.

[Fatjack-jygs]

I did enjoy that. I have not done any Maths for far too long. I hardly know any of it any more.

[ybodoN]

Easy solution: Heron's formula gives the area of the triangle.Then the radius of the circle is abc / 4A.

[tombufford]

At a quick glance: The centroid of the triangle and the three medians are coincident. where h is the height. X1 and Y1 are the x and y coordinates from A of the Centroid. X1 = 14/2 = 7. Y1 = h/3. AD =x . r^2=7^2+h^2/9, x^2+h^2=169 and h^2=225-(14-x)^2. R^2=49+(169-x^2)/9. h^2=29-28x-x^2. h^2=169-x^2 then 140-28x=0 and x=5. Then h = 12 and the radius = SQRT(49+ 144/9)=8.1

[prashant]

Hello sir..I m from India..and watch your videos...I really like it and encourage others to watch

[weipenglim]

You can use cosine rule to solve for angle alpha

[chintamanisatyamurthy]

Very well explained. Though different methods r also there, the way u explained in ur own method is superb.

[uwelinzbauer]

My idea was: the perpendicular lines through the mids of the sides of a triangle intersect in the center point of the outer circle. To find the radius of the circle, I used the cosine and the sine rules.
Luckily I found that same correct solution in the end 😅
Nice challenge, a little hard to work out, but challenges make us 💪 😀
Greetings!

[swzocyx]

Cosine rule to find one angle then doing sine rule =2R and you find R

[shirish]

Join OA and OB. OA= OB = R. Angle AOB = twice of angle ACB. Using cosine law for triangle ABC, we can find cos C. From here, find cos 2C, that is, cos AOB. Now again use cosine law for triangle AOB to find R.

[CalvinLXVII]

Un ejercicio muy interesante!
Saludos!

[ahmadesteitieh]

Find the area of the triangle using half perimeter then deduce the length of the heght you drew and find the radius as you proceeded