Explore Angle Theorems with Expert Help

What is the measure of $∡ x$ in the figure below?
For reference: In the figure shown P and Q are points of tangency and $\overset{⌢}{B C} + \overset{⌢}{F E} = 130^{o} .$ . Calculate "x".

Licinilg 2022-08-24

One of the rays of the inscribed angle is the diameter.
Given: Circle O
BC is a diameter.
Prove: $m ∠ A C B = \frac{1}{2} m A B$

Raelynn Nolan 2022-08-22

How to prove the directed angle cyclic quadrilateral theorem?
"Prove that 4 points A,B,X,Y, no 3 collinear, are concyclic if and only if $∡ X A Y = ∡ X B Y$
(Where $∡$ stands for directed angle $\mod 180^{\circ}$ )"
How does a proof look like that this actually matches the "normal" cyclic quadrilateral theorem?

ximblajy 2022-08-22

Finding angle in a triangle with one median and an isosceles triangle in it
In the following figure $A F = B D = D C$ and $A E = E F$ . Find the angle $α$ .

Paulkenyo 2022-08-22

Geometry question about bisecting angles
Let $△ A B C$ be a triangle and let O be its circumcentre. Let D and M be points on BC such that AD is perpendicular to BC and AM bisects the angle at A. Prove that AM bisects the $∠ O A D$ .
What theorems are helpful for solving this question?

Licinilg 2022-08-21

How do you find a point on a line bisecting an angle in three-dimensional space?
Given the x, y, z coordinates of three points $P_{1}, P_{2}, P_{3}$ with the angle between them being $∠ P_{1} P_{2} P_{3}$ , how do you find a point, say at a distance of 1 from $P_{2}$ , on the line that bisects the angle?I know from the angle bisector theorem that the point must be equidistant from the the vector $(P_{3} - P_{2})$ and $(P_{1} - P_{2})$ , but I can't seem to figure out how to find such a point in 3-space.

Miguel Mathis 2022-08-21

How to use congruence and angle bisector theorem for this geometry question involving isosceles triangle?
Here is the diagram for the question:

In triangle $△ A D C$ , $| A B | = | A C | = 8$ and $| N C | = 6$ . AN is the bisector of $∡ B A C$ . $∡ A D C = 2 \cdot ∡ B C D$ . $| D N | = x$ . Find x.

dyin2be0ey 2022-08-20

In right $Δ A B C$ , $∠ C = 90^{\circ}$ . E is on BC such that $A C = B E$ . D is on AB such that $D E ⊥ B C$ . Given that $D E + B C = 1$ and $B D = \frac{1}{2}$ , Find $∠ B$ .

Braeden Valenzuela 2022-08-20

Let $△ A B C$ be a triangle with angle bisector CL $(L \in A B)$ and median CM $(M \in A B)$ . I should find LM if $B C = a, A C = b, A B = c (a > b)$ .

torfuqx 2022-08-20

So I have a right angled triangle as shown in the image

What I have to prove is that the angle C is not 60 degrees. I am not sure if I have to use Pythagoras theorem or something else.

monopolutk 2022-08-19

Triangle angle bisector problem: Finding area

Area $△ A B C$ =?
How to apply this theorem?

granuliet1u 2022-08-17

Let $△ A B C$ have $A B = 15$ , $B C = 14$ , and $C A = 13.$ . Let $ℓ_{1}$ be the angle bisector of $∠ A B C$ and let $ℓ_{2}$ be the angle bisector of $∠ B A C .$ . If the projection of B onto $ℓ_{2}$ is Q and the projection of A onto $ℓ_{1}$ is P find PQ.

ferdysy9 2022-08-17

Proving the Secant Angles in the Circle
How to prove the theorem of angles in the circle. Like this image here:

How prove that the angle X is the half of the sum of both angles' measurement of the Arc AC and Arc BD? This image here:

How prove that the angles A is the half of the difference of both angle measurements of Arc BC and Arc DE?

Ledexadvanips 2022-08-17

Use vectors to show that A(3,0,2), B(4,3,0), and C(8,1,-1) are vertices of a right triangle. At which vertex is the right angle?

Katelyn Reyes 2022-08-16

Get angle of point in circle with center (0, 0).
I have a circle with a centre at position (0, 0) and I have a point in the circle at (-5, 2). How can I get the angle of the point towards the centre?

Garrett Sheppard 2022-08-15

"Inverse" of the inscribed angle theorem.
While doing geometry problem I encountered something I would call "inverse" of inscribed angle theorem. At first I wanted to state it like this:
Given $△$ ABC and point O such that $∠$ BOC = 2 $∠$ BAC it implies that O is the centre of the circle described on the $△$ ABC
But of course it is easy to show that this statement doesn't hold. But on my native language forum I found that this theorem should hold:
Given $△$ ABC and $∠$ A = $α$ and point O lying on the perpendicular bisector of the segment BC with $∠$ BOC = 2 $α$ and point O lying on the same side of line BC as point A then point O is the centre of the circle described on $△$ ABC

Maia Pace 2022-08-15

Euclidean Version of Pappus's theorem
Let A, B, C, be points on a line l, and let A′, B′, C′ be points on a line m. Assume AC′∥A′C and B′C∥BC′. Show that AB′∥A′B.

Jenny Stafford 2022-08-14

Two circles cut orthogonally in A and B. A diameter of one of the circles is drawn cutting the other circle in C and D. Prove that $B C \cdot A D = A C \cdot B D$ .

gladilkamwy 2022-08-14

Angle chasing to show three points are collinear.
Let ABC be an acute triangle with circumcenter O and let K be such that KA is tangent to the circumcircle of $△ A B C$ and $∠ K C B = 90^{\circ}$ . Point D lies on BC such that KD||AB. Show that DO passes through A.

popljuvao69 2022-08-14

Solution of triangles in Non-Euclidean geometry with restrictions
In triangle $A B C, A B > A C$ . D is a point on AB such that $A D = A C$ .
Prove that $∠ A D C = \frac{∠ B + ∠ C}{2}$ and $∠ B C D = \frac{∠ C - ∠ B}{2}$ .
Solving this problem in Euclidean geometry is very easy. But how can it be solved with the following restrictions?
1) Parallel postulate (i.e. properties of parallel lines ) cannot be used.
2) Theorems proved using properties of parallel lines cannot be used.
3) The problem has to be solved the way euclidean geometry problems are solved. Cartesian Geometry cannot be used.
If not solvable, why cannot be?

Angles are an important part of mathematics, and angle theorems help us understand the properties of angles and how they relate to each other. Angle theorems allow us to calculate the size of angles and to determine the relationships between them. They are used in geometry and trigonometry to help us solve various problems. Some of the most common angle theorems include the angle sum theorem, the exterior angle theorem, and the triangle angle bisector theorem. These theorems can help us calculate angles in triangles and quadrilaterals, as well as other shapes. Angle theorems are very useful in mathematics and can help us understand the properties of angles and how they relate to each other.

Angle theorems Uncovered: Discover the Secrets with Plainmath's Expert Help