All Questions
72
questions
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On Ratios in Isosceles Triangles
It is known that the formula for the perimeter $P$ of an isosceles triangle on a plane is $$P=2L+B$$, where $L$ is the length of the leg and $B$ is the length of the base. Now, let us study some ...
- 356
7
votes
3
answers
435
views
Ratios of lengths in a triangle
Problem I'm trying to solve:
My Attempt:
To be honest, I don't have any clue on how to solve it and the method I'm about to give is severely overcomplicated. We first isolate triangle $\triangle BEG$ ...
- 728
0
votes
1
answer
41
views
Is Basic Proportionality theorem applicable to trapezium? [closed]
I was studying vectors and came up with this question
Show that the line joining the midpoints of two non parallel sides of a trapezium is parallel to the parallel sides and is equal to half of their ...
- 13
0
votes
1
answer
173
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Find the ratio of the perimeter of a square and of a triangle.
Problem:
Let the square $ABCD$ be on the side $l$ and the points $E$ and $F$ on the sides $BC$ and $CD$ respectively so that $\angle EAF= 45$. Find the ratio between the perimeter of the square and ...
- 748
1
vote
4
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273
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HELP Let ABC an isosceles right triangle with ABC = 90°. Consider the point P on AB such that $\frac{PA}{PB}=2$. Show that $PA\cdot BP=BQ\cdot BG$.
Let ABC be an isosceles right triangle with ABC = 90°, M and N the midpoints of sides BC and AC, and G is BN intersected by AM. Consider the point P on AB such that $\frac{BM}{BP}=2$. If BN intersects ...
user1104319
0
votes
2
answers
84
views
Ratio of lengths $QD/QC$ where $Q$ belongs to the side $CD$ of a square
Let ABCD be a square, M the middle of (AB), N the middle
of (AD), {P} = CN ∩ DM and {Q} = AP ∩ CD. Calculate $QD/QC$.
You can see down my idea and the drawing::
Okey! So first of all i thought of the ...
user1104319
1
vote
2
answers
130
views
Triangle with side lengths and three tangent circles, finding ratio of lengths $KF/KE$
Triangle $ABC$ has side lengths $AB=7, BC=8,$ and $CA=9.$ Its incircle $\Gamma$ meets sides $BC,CA,$ and $AB$ at $D,E,F$ respectively. Let $AD$ intersect $\Gamma$ at a point $P \neq D.$ The circle ...
- 466
2
votes
2
answers
570
views
Ratio of radii of two circles inscribed in a right isosceles triangle.
There is a right isosceles triangle $\triangle ABC$ with the vertex $B$ facing the hypotenuse.
A circle is inscribed into the triangle with radius $r_1$, then another circle with radius $r_2$ is ...
- 35
0
votes
1
answer
43
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How is it the possible to find the ratio of the sides in the picture
I am trying to calculate the ratio of CE(green) to BE(blue). Given that FC:FM = 3:1 and it's an equlateral triangle.
I have tried drawing triangles to get an approximation, and I have drawn it in the ...
- 187
3
votes
2
answers
584
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Find area of Pentagram : Regular Pentagon if $AP : PQ = m:1$
While I was doing an Olympiad geometry sum in Sri Lanka I found this question
A pentagram is a regular pentagon with its sides extended to their point of intersection. In the
pentagram ABCDE shown ...
- 773
2
votes
3
answers
235
views
School-level vector question for finding length ratios in a triangle
https://revisionmaths.com/sites/mathsrevision.net/files/imce/Questionpaper-Paper1H-November2018.pdf
$OAB$ is a triangle. $OPM$ and $APN$ are straight lines. $M$ is the midpoint of $AB$ and $N$ is on ...
- 131
6
votes
6
answers
545
views
Points on the hypotenuse of a right-angled triangle
Points $K$ and $L$ are chosen on the hypotenuse $AB$ of triangle $ABC$ $(\measuredangle ACB=90^\circ)$ such that $AK=KL=LB$. Find the angles of $\triangle ABC$ if $CK=\sqrt2CL$.
As you can see on the ...
0
votes
1
answer
104
views
Ratio of two line segments in a special right triangle
So I had this question in my mind for a while.
At first, I tried using a bunch of theorems such as the Law of Sines, the Law of Cosines, and similarity. I got the answer $\frac{a}{a-1}$, but then I ...
- 141
0
votes
2
answers
1k
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Inscribed circle of an isosceles triangle
In a triangle $ABC$, $AC = BC = 24$ and a circle with center $J$ is inscribed. If $CH$ is altitude $(CH\perp AB,H\in AB)$ and $CJ:CH=12:17$, then find the length of $AB$.
Triangle $ABC$ is isosceles ...
- 5,352
5
votes
2
answers
304
views
Ratio of area of triangle and hexagon
I am looking for the proof of the following claim:
Claim. If the sides of the triangle are partitioned into $n$ equal segments for $n$ an even integer and each division point adjacent to the ...
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