7
votes
4answers
192 views

Construction of a triangle

I need to construct a triangle with given information: $c = 6$, $h = 4$ and $\alpha - \beta = 30º$. I'll put approximate result for any clarification.
1
vote
1answer
41 views

Is the given triangle unique?

I was reading Polya's How to Solve It when I came across the following problem. Construct a triangle with an angle, the length of altitude through that angle and the perimeter of the triangle given. I ...
2
votes
2answers
122 views

triangle construction given side, angle and median

I can't figure out the solution to this, it looks to me like it doesn't have any solution but I need some proof. problem: Construct a triangle ABC with given $a=6 cm$ $\alpha=75^\circ $ and ...
3
votes
3answers
116 views

Construct triangle given inradius and circumradius

If we know the inradius $r$ of a triangle and the circumradius $R$ we can find out the distance between the incircle $I$ and the circumcircle $O$: $OI^2 = R^2-2Rr$. Therefore we can draw the incircle ...
4
votes
1answer
114 views

Is it possible to approximate all angles with certain pythagorean triples?

With sticks $a,b$ and $c$ of length $3,4$ and $5$, you able to draw a right (tri)angle. But are also able to construct an angle $\cos\alpha=\frac35, \alpha=\arccos(\frac35)=$$53.13010...^°$. Is it ...
6
votes
2answers
697 views

Equilateral triangle geometric problem

I have an Equilateral triangle with unknown side $a$. The next thing I do is to make a random point inside the triangle $P$. The distance $|AP|=3$ cm, $|BP|=4$ cm, $|CP|=5$ cm. It is the red ...
4
votes
2answers
519 views

Construct a triangle given one side, its height and inradius

I've been scratching my head with this problem: "Draw a triangle given one of its sides, the height of that side and the inradius." Now, I can calculate the area and obtain the semiperimeter. From ...
1
vote
3answers
80 views

Prove that altitude² = pq?

The following is a question for my math class. I just cannot figure it out. Given is that: h is the altitude that divides the longest side of this right triangle into p and q. Question: Prove that ...
5
votes
4answers
807 views

Constructing a triangle given three concurrent cevians?

Well, I've been taught how to construct triangles given the $3$ sides, the $3$ angles and etc. This question came up and the first thing I wondered was if the three altitudes (medians, ...
8
votes
2answers
703 views

Sangaku: Show line segment is perpendicular to diameter of container circle

"From a 1803 Sangaku found in Gumma Prefecture. The base of an isosceles triangle sits on a diameter of the large circle. This diameter also bisects the circle on the left, which is inscribed so that ...