Recent questions in Euclidean Geometry

Elementary geometryAnswered question

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.

Elementary geometryAnswered question

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.

Elementary geometryAnswered question

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?

What´s the length of the segment AC in the triangle below?

Elementary geometryAnswered question

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.

Elementary geometryAnswered question

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 $\frac{KF}{KE}}.$ .

Elementary geometryAnswered question

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.

Elementary geometryAnswered question

tuehanhyd8ml 2022-05-15

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

Elementary geometryAnswered question

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.

Elementary geometryAnswered question

Waylon Mcbride 2022-05-13

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

Elementary geometryAnswered question

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?

Elementary geometryAnswered question

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 $OP=OQ$

Elementary geometryAnswered question

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.

Elementary geometryAnswered question

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

Elementary geometryAnswered question

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

Elementary geometryAnswered question

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?

Elementary geometryAnswered question

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.

Elementary geometryAnswered question

Esther Hoffman 2022-05-03

Find all points P such that $\frac{BC}{P{H}_{A}}+\frac{AC}{P{H}_{B}}+\frac{AB}{P{H}_{C}}$ is minimum.

Elementary geometryAnswered question

kadetskihykw 2022-05-02

In triangle ABC, $\mathrm{\angle}A=20\xba$ and $AM=CN=CB$ . Find angle $\mathrm{\angle}MBN$ ?.

Elementary geometryAnswered question

Davian Lawson 2022-05-02

In a triangle ABC, the interior cevian CM is drawn, so that $CM=AB$ ; Knowing that the measure of $\mathrm{\angle}A=30\xb0$ and $\mathrm{\angle}B=100\xb0$ . Calculate the measure of $\mathrm{\angle}MCB$ .

Elementary geometryAnswered question

Jordon Haley 2022-04-06

What term/identity/theorem states that given a triangle the largest angle must be opposite the longest side?

The majority of Euclidean Geometry problems and solutions that you will find online will be unclear as you can only read the graphs and the equations that will have little to no explanations. It is one of the reasons why we have collected the list of questions and the answers that will help you to see the rationale. Start by taking at least one Euclidean geometry example and add either a graphical or word problem. It will let you understand the explanations and continue with your task by offering more than one solution (meaning the verbal part and the graphs).