Questions tagged [triangles]
For questions about properties and applications of triangles.
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Orthocenter: The "Bad Boy" of Distinguished Points in a Triangle
It is a well-known fact that the altitudes of a triangle $ABC$ (with vertices $A,B,C)$ intersect at exactly one point, the orthocenter. The proof known to me (see eg here) involves the construction of ...
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How do I determine angles and lengths of a triangle if I'm only given one angle and one side length. [closed]
I just don't think I can if given angles A, B, and C (where A and B are unknown and C = 90 deg) and sides a, b, and c--the sides opposite the angles--where side a is 10 in and sides b and c are ...
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Olympiad geometry problem with angles [closed]
Triangle ABC has a right angle at A. Altitude AD has length 20. The bisector of angle B meets AD at K. If angle ACK= 2angle DCK, find KC. This is an olympiad practice problem which I am trying to ...
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How can I solve this geometry problem? [closed]
Triangle ABC is equilateral triangle. M is on side AB and P is on side CB such that MP || AC. D is the centroid of triangle MBP and E is the midpoint of PA. Find the angles of triangle DEC.
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In a geodesic triangle, is the longest side opposite to the largest angle?
If I have a complete (smooth) Riemannian manifold $(M,g)$ and three points on it, that I connect with distance minimizing geodesics, will the longest edge be opposite to the largest angle?
In ...
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What are sides of triangle if angular trisector trisects opposite side in particular segments [closed]
In triangle ABC, AD and AE trisect ∠BAC. The lengths of BD,DE and EC are 2,3 , and 6 , respectively. Find the length of the shortest side of △ABC .
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How to find hypotenuse from the distance of the centroid to that point that is the right angle [closed]
I have a problem that says: In Rt△ABC, ∠C= 90°, point G is the centroid of Rt△ABC. If CG=6, then the length of the Hypotenuse is_______.
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Finding the area of a triangle knowing the coordinates of the midpoints of its medians [closed]
The midpoints of the medians of $\triangle ABC$ are $(1,2)$, $(4,4)$, and $(2,8)$. Find the area of the $\triangle ABC$.
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Is there is a formula to calculate the coordinates of the orthocenter of a triangle?
I'm trying to find the coordinates of the orthocenter (the intersection point of all altitudes) of a triangle given its vertices' coordinates $A=(x_1, y_1), \ B=(x_2, y_2) , \ C=(x_3, y_3)$.
I ...
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Proof using Converse of Thales Theorem for isosceles right-angled triangle
Let $ABC$ an isosceles right-angled triangle with the right angle at $C$. Suppose that the points $D$ and $E$ lie outside the triangle on the half-line $AC$ and $CB$, respectively (see picture).
Let ...
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Maximum area a traingle can have which can fit inside a circle of radius $r$? [duplicate]
So what is the maximum area of a triangle which can fit inside a circle of radius r?
My first approach: We know that $\text{ Circumradius }=\frac{abc}{4×\text [area-of- triangle}$ (here abc are side ...
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2-D scalene obtuse triangle trigonometry.
I am struggling with this trigonometry question:
I tried using the cosine law with angle DBC
$a^2 = b^2 + c^2 - 2bc \cos A$ but you need to know the measure of the angle.
In terms of the angle Φ, the ...
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Largest Area Triangle in the Vesica Piscis
I can place any three points in or on a vesica piscis1. I wish to find the triangle of maximum area. I know the area of the vesica piscis is $(\frac{2π}{3}-\frac{\sqrt{3}}{2})d^2$ (where d is the ...
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Knowing a side, the inradius, and the circumradius of a triangle, find the other two sides [closed]
I need help with this easy triangle problem:
We know:
One of the sides a = 16 cm.
The inradius r = 6cm.
And the circumradius R = 17 cm.
That's all.
We must find the lengths of the other two sides.
...
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Determine the angle $\angle DEC$ in a triangle (Euclidean Geometry)
Any ideas how to find the angle $\angle DEC$ in the following situation shown in the image:
In the above figure we have that $\angle BAC = 90, \angle ABD = \alpha, \angle DBC = 2\alpha$, and $\angle ...
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