# Our Euclidean Geometry Example will Make You Pro in Geometry!

Recent questions in Euclidean Geometry
Kyla Ayers 2022-06-22

## Let a circle $\omega$ (not labelled in the graph) centered at P tangent to AB, and T is point of tangency. $\mathrm{\angle }APB={90}^{\circ }$ . Let K (not labelled in the graph) be some point on the circle $\omega$ , the semicircle with diameter BK intersects PB at Q. Let R be the radius of that semi-circle. If $4{R}^{2}-AT\cdot TB=10$ and $PQ=\sqrt{2}$ , calculate BQ.

Quintin Stafford 2022-06-20

## For reference: In the drawing, T is the point of tangency, $LN||AT$, $OH=4$ and $L{N}^{2}+A{M}^{2}=164$ . Calculate HN.

Arraryeldergox2 2022-06-13

## In the triangle $\mathrm{\angle }A$ is right and D is a point on the side AC such that the segments BD and DC have length equal to 1m. Let F be the point on the side BC so that AF is perpendicular to BC. If the segment FC measures 1m, determine the length of AC.What´s the length of the segment AC in the triangle below?

Roland Manning 2022-06-12

## Find the geometric place of the points from where as we draw the tangents at ellipse $\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1$ , they are perpendicular.

Estrella Le 2022-06-03

## Triangle ABC has side lengths $AB=7,BC=8,$ and $CA=9.$ Its incircle $\mathrm{\Gamma }$ meets sides BC, CA, and AB at D, E, F respectively. Let AD intersect $\mathrm{\Gamma }$ at a point $P\ne D.$ . The circle passing through A and P tangent to Γ intersects the circle passing through A and D tangent to $\mathrm{\Gamma }$ at a point $K\ne A.$. Find $\frac{KF}{KE}.$ .

Kallie Arroyo 2022-06-02

## Let ABC be an acute angled triangle with circumcenter O. A circle passing through A and O intersects AB, AC at P, Q respectively. Show that the orthocentre of triangle OPQ lies on the side BC.

tuehanhyd8ml 2022-05-15

## What's the ratio between the segments $\frac{AF.BG}{FG}$ in the figure below?

Edith Mayer 2022-05-14

## Show that the circumscribed circle passes through the middle of the segment determined by center of the incircle and the center of an excircle.

Waylon Mcbride 2022-05-13

## Find the area of a triangle with vertices $\left(0,1,1\right),\left(-1,-1,2\right),\left(2,3,1\right)$

tiyakexdw4 2022-05-10

## Suppose I have 4 unit vectors in 3D and I know all the ${}^{4}{C}_{2}=6$ angles between them. These angles provide the complete description of this group of vectors. Now, I want to add anther unit vector to the mix. How many additional angles do I need to uniquely identify this new vector?

fetsBedscurce4why1 2022-05-10

## If K is the midpoint of AH, $P\in AB$, $Q\in AC$ and $K\in PQ$ such that $OK\perp PQ$ , then $OP=OQ$

Peia6tvsr 2022-05-10

## A convex quadrilateral ABCD is inscribed and circumscribed. If the diagonals AC and BD are perpendicular, show that one of them divides the quadrilateral into two congruent right triangles.

Waylon Mcbride 2022-05-10

## Given: ABCD is a parallelogram,$\overline{AM},\overline{BN}$ angle bisectors,$DM=4\phantom{\rule{thinmathspace}{0ex}}\text{ft.}$, $MN=3\phantom{\rule{thinmathspace}{0ex}}\text{ft.}$Find: the perimeter of ABCD

uto2rimxrs50 2022-05-08

## Show that the orthocenter of ABC lies on ${P}^{\prime }{Q}^{\prime }$ , where ${P}^{\prime },{Q}^{\prime },{R}^{\prime }$ are the symmetric points of M to this sides of the triangle, M on circumscribed

encamineu2cki 2022-05-08

## In a bichromatically colored plane, is it always possible to construct any regular polygon such that all vertices are the same color?

Daphne Haney 2022-05-07

## Given rectangle ABCD with K the midpoint AD and $AD/AB=\sqrt{2}$ , find the angle between BK and diagonal AC.

Esther Hoffman 2022-05-03