# Tagged Questions

For questions about properties and applications of triangles

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### Similar Triangles--Find the measurement of the unknown side [closed]

This is a question I know I got wrong on a final exam in a very easy class for teaching elementary geometry/prep for Praxis II. I actually received a 99% average in the entire course because of the ...
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### A geometry problem hinting similarity of triangles .

I recently came across a geometry problem , published in an local magazine(publishing at high school and under graduate level) and was under Difficulty : Hard sub heading. Consider a $\triangle ABC$ ...
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### Prove for Pedal & Isosceles triangle.

The tangents at two points $B$ and $C$ on a circle meet at $A$. Let $A_1B_1C_1$ be the pedal triangle of the isosceles triangle $ABC$ for an arbitrary point $P$ on the circle, as shown below. Then ...
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### Unique Trianlge Count sequence

Consider a simple graph $G(V,E)$, such that $V = \{1,2,\dots, n\}$. We can define the triangle count of a vertex as follows: $\Delta(v) =$ Number of triangles in the graph such that $v$ is one of ...
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### Counting number of points making angle < 90

I have a around 1000 points and 1000 segments in the form of $(x_1, y_1, x_2, y_2)$ meaning the segment starts at coordinate $(x_1, y_1)$ and finishes at $(x_2, y_2)$. For each line i want to know how ...
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### Can you solve this geometric question on triangles? [closed]

In a triangle $ABC$, $D$ is a point on the side $BC$.Given: $AD=10$,$BD=DC=8$ and $BC*AD=6$.What is the length of $BC$? a.$5$ b.$10$ c.$15$ d.$20$ That was asked in a newspaper quiz.
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### Get second vertex of isosceles triangle [closed]

Given the equal sides of the triangle and the angle $\theta$ between them as well as the other 2 vertices of the triangle how do I get the second base vertex coordinates. Sorry for my poor drawing. <...
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### Triangle - Trapezoid [Geometry]

I'm having trouble with following assignment: "Sides of triangle are $13$, $14$, and $15$. Line parallel to the longest side cuts through the triangle and forms a trapezoid which has perimeter of $39$...
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### Area of all triangles involved in a big triangle.

I have a big triangle made up of several small triangle as depicted in picture given below. Suppose, there is one generic triangle of this shape which is formed by joining points arranged in n rows....
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### Sum of Area of Circles. [duplicate]

A circle of radius x cm is inscribed in an equilateral triangle and is tangent at three points. Three smaller circles are inscribed so that they are each tangent to two sides of the triangle and to ...
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### Find equal side lengths for isosceles triangle from middle angle and area?

I know that this is a really easy question, but I am looking for the answer to this question: The area of this isosceles triangle is 5cm squared. The angle ABC is 22 degrees. Work out ...
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### Problem on circles, tangents and triangles

Let $c_1,c_2,c_3$ be three circles of unit radius touching each other externally. The common tangent to each pair of circles are drawn (and extended so that they intersect) and let the triangle formed ...
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### How to solve this $80^\circ$-$80^\circ$-$20^\circ$ triangle ($60^\circ+20^\circ$ and $70^\circ+10^\circ$ variant)? [duplicate]

A friend of mine asked me for help with a math problem and I struggled with this for over an hour. I told him sorry, and I felt bad. It's been bugging me now for hours. I don't even so much care for ...
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### Geometry (ratio of subdivided length in a triangle)

In triangle ABC, label X on AB and Y on AC such that AX : XB = CY : YA = 2 : 1. Extend XY and BC such that they meet at point Z. Find ZB : ZC.
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### Find the sides of the triangle.

The triangle with sides $8-15-13$ has a $60^{\circ}$ angle. The triangle with sides $11-35-31$ also has a $60^{\circ}$ angle. Find a triangle $x-y-403$ where $x$ and $y$ are relatively prime positive ...
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### Finding area of triangles [closed]

In a triangle, the average of any two sides is $6 cm$ more than half of the third side , then find the area of the triangle (in$\ cm ^ {2}$)
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### Finding Area of the Triangle [closed]

In the figure, the ratio of AD to DC is 3 to 2. If area of $\Delta ABC$ is 40 $cm ^ {2}$ , what is the area of $\Delta BDC$
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### If $a^2 + b^2 = c^2$, then $a^3 + b^3 < c^3$, for $a$, $b$, $c$ the sides of a triangle

If $a$, $b$, $c$ are the sides of a triangle where $a^2 + b^2 = c^2$, prove that $a^3 + b^3 < c^3$. I've tried triangle inequality, but I am stuck.
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### Drawing triangle

follow the picture: $m$,$p$ and $Q$ are midpoints of segments we want to draw the triangle and we only have the lengh of $AM$,$BQ$ and $CP$ How to draw the triangle?
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### A triangle in a square

The following quadrilateral is a square also there are some known angles.prove that The segments of the inner triangle are equal. My Attempt:If we name the inner point $O$ then two triangles $AOD$ ...
The inner circle of triangle $ABC$ touches $BC$ at $D$ . Show that the circles inscribed in triangles $ABD$ and $CAD$ touch each other.