Euclidean Geometry Problems and Solutions from Experts

If the very early Greeks has decided that the tangent line to a circle meets at a line segment, rather than a point, what simple contradiction about triangles could be proved?

wendi1019gt 2022-08-05

The perimeter of a triangle is 76cm. Side a of triangle is twice as long as side b. side c is 1cm longer than side a. find the length of each side.

sunnypeach12 2022-08-02

Remark 2: Euclid's proof amounts to solving the above equation. Construct the square ABCD, given segment AB. Let E be the midpoint of AD. Construct the point of intersection, F, of the dircde centered at E of radius EB and the extension of segments DA, as shown. Now construct square AFGX, all of whose sides have length AF, with X on segment AB.
Claim: X is the desired point.
Notice that $A E = \frac{1}{2} A D = \frac{1}{2} a$
(ii)
Apply the Pythagorean Theorem to the right triangle ABE to find EB in terms of a.
EB=______

equissupnica7 2022-07-28

If the non-base angle of angle of anisosceles triangle has a measure of 70o, what is themeasure of each base angle?
How many diagonals does a decagon have?

Kenya Leonard 2022-07-28

For the line given by, y = 3x , find the slope of a line that is:
a) Parallel to the given line: m_{parallel} =
b) Perpendicular to the given line: m_{perpendicular} =

Deromediqm 2022-07-26

For the line given by, y = -4 x - 4 , find the slope of a line that is:
a) Parallel to the given line: m_{parallel} =
b) Perpendicular to the given line: m_{perpendicular} =

hornejada1c 2022-07-15

Let $X = {(x, y) \in R^{2} ∣ y = 0 or x \geq 0}$ and $f : X \to R$ defined by $f (x, y) = x$ . I want to find $C \subset X$ closed such that $f (C) \subset R$ isn't closed. How to prove that f is a closed map?

therightwomanwf 2022-07-11

Given two noncoplanar lines p and q, and a point A, does there always exist a line that passes through p, q and A?

Sam Hardin 2022-07-10

$\frac{1}{a + b} + \frac{1}{a + c} = \frac{3}{a + b + c}$ in a triangle
Find the angle $α$ of a triangle with sides a, b and c for which the equality

pouzdrotf 2022-07-05

Show that the area of triangle $S_{A B C} = R \times M N$

kolutastmr 2022-07-04

I was reading a paper on hyperbolic pascal triangle and the author stated that for Schlafli symbol ${p, q}$ , if $(p - 2) (q - 2) = 4$ , it determines the Euclidean mosaic. For $(p - 2) (q - 2) < 4$ a sphere is determined and for $(p - 2) (q - 2) > 4$ a hyperbolic mosaic is defined.
On the nature of mosaic specified by Schlafli symbol ${p, q}$ ?

Nickolas Taylor 2022-07-04

Show that $x (t) = 2 r \cos^{2} (t)$ , $y (t) = 2 r \sin t \cos t$ is a regular parametrization of the real circle of radius r, centre (r, 0).

kolutastmr 2022-07-01

The area of a triangle with sides $59, 37, 12 \sqrt{5}$

Banguizb 2022-06-30

Let $△ A B C$ and E, D on $[A B]$ and $[A C]$ s.t. BEDC is inscribable. Let $P \in [B D], Q \in [C E]$ , s.t. AEPC and ADQB are also inscribable. Show that $A P = A Q$ .

mravinjakag 2022-06-27

Prove: If the sum of the angles of a triangle is a constant n, then $n = 180$ and thus the geometry is Euclidean

Yahir Crane 2022-06-27

If in a tetrahedron ABCD the heights are congruent and A is projected on the (BCD) plane in the orthocenter, ABCD is a regular tetrahedron

Zion Wheeler 2022-06-25

Quadrilateral ABCD satisfies $\bar{2 A B} = \bar{A C}$ , $\bar{B C} = \bar{\sqrt{3}}$ , $\bar{B D} = \bar{D C}$ and $< B A C = 60$

watch5826c 2022-06-24

Given a point $(x_{0}, y_{0})$ and a radius r, how do you find the set of all circles that have that radius that pass through the point?

Armeninilu 2022-06-23

Let H be the orthocenter of acute $△ A B C .$ . Points D and M are defined as the projection of A onto segment BC and the midpoint of segment BC, respectively. Let $H^{'}$ be the reflection of orthocenter H over the midpoint of DM, and construct a circle $Γ$ centered at $H^{'}$ passing through B and C. Given that $Γ$ intersects lines AB and AC at points $X \neq B$ and $Y \neq C$ respectively, show that points X, D, Y lie on a line.

Devin Anderson 2022-06-22

In the interior of a triangle ABC, a point P is marked in such a way that: $P C = B C$ and the measure of the angle PAB is equal to the measure of the angle PAC which is $17 °$ . calculate the measure of angle PCB, if the measure of angle $B = 107^{o}$

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).

Elementary geometry

Our Euclidean Geometry Example will Make You Pro in Geometry!