# Angle theorems problems with answers

Recent questions in Angle theorems
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 $\mathrm{△}$ ABC and point O such that $\mathrm{\angle }$ BOC = 2 $\mathrm{\angle }$ BAC it implies that O is the centre of the circle described on the $\mathrm{△}$ ABCBut 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 $\mathrm{△}$ ABC and $\mathrm{\angle }$ A = $\alpha$ and point O lying on the perpendicular bisector of the segment BC with $\mathrm{\angle }$ BOC = 2 $\alpha$ 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 $\mathrm{△}$ ABC

Maia Pace 2022-08-15

### Euclidean Version of Pappus's theoremLet 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

### 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 $\mathrm{△}ABC$ and $\mathrm{\angle }KCB={90}^{\circ }$. 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 restrictionsIn triangle $ABC,AB>AC$. D is a point on AB such that $AD=AC$.Prove that $\phantom{\rule{thinmathspace}{0ex}}\mathrm{\angle }ADC=\frac{\mathrm{\angle }B+\mathrm{\angle }C}{2}$ and $\mathrm{\angle }BCD=\frac{\mathrm{\angle }C-\mathrm{\angle }B}{2}$.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?

motsetjela 2022-08-13

### You have triangle $\mathrm{△}ABC$ which is orthogonal $\mathrm{\angle }C={90}^{o}$ with circle with center O inscribed in it. If KL is the diameter, KL∥AB, $KM\perp AB$ and $LN\perp AB$. Find angle $\mathrm{\angle }MCN$.

janine83fz 2022-08-13

### Question about the angle $\theta$ Green's theoremGiven $Q\left(x,y\right)=x\cdot {y}^{2}+y\mathrm{ln}\left(x+\sqrt{{x}^{2}+{y}^{2}}\right)$ and $P\left(x,y\right)=\sqrt{{x}^{2}+{y}^{2}}$ calculate the integral ${\int }_{C}P\phantom{\rule{thinmathspace}{0ex}}dx+Q\phantom{\rule{thinmathspace}{0ex}}dy$ while $C=\left(x-1{\right)}^{2}+\left(y-1{\right)}^{2}=1$why $\theta$ should be until $2\pi$?

dredyue 2022-08-13

### How can the sin/cos/tan values in a right angle be negative?A and B are both obtuse angles such that $\mathrm{sin}\left(A\right)=\frac{5}{13}$ and $\mathrm{tan}B=\frac{-3}{4}$. Find exact values for $\mathrm{sin}\left(A+B\right)$.Assuming that the pythagorean theorem is used to answer the question, how is it possible that the values for $\mathrm{tan}B=\frac{-3}{4}$? (That is, a 3-4-5 right angle triangle... how can a side be negative?)

ahredent89 2022-08-13

### Prove that the intersection angle between the Simson lines of two triangles inscribed in the same circle it's the same for any point.Suppose the triangles ABC and DEF share the circuncircle C, and P and Q are any diferent points on C. Let l, m be, the Simson lines of P related to ABC and DEF, and p, q the Simson lines of Q related to ABC and DEF, then i must prove the angle between l and m equals the angle between p and q.I just have one Theorem about the Simson line:Theorem: Let P, Q be two points on the circuncircle, C, of the triangle ABC. Let l, m be their respective Simson's lines. Then the angle between l an m equals to the half of the central angle POQ, where O is the center of C.

makeupwn 2022-08-13

### How to find an angle between the extension of a diameter and a chord in a semicircleO is the center of the semicircle, if $\mathrm{\angle }EOD={45}^{\circ }$ and $OD=AB$, find $\mathrm{\angle }BAC$

Moselq8 2022-08-12

### Integral over solid angle in Cartesian coordinatesI have an integral that is an average of some (unknown) function f over solid angle:

Brandon Monroe 2022-08-12

### Finding a triangle angle based on side length equalityConsider the triangle ABC with angle A being 70 degrees, and the side lengths satisfying:$B{C}^{2}=AC\left(AB+AC\right)$Is there any intuitive way of finding the measure of angle B?

Sydney Stein 2022-08-12

### Pythagoras: Get b when only a and angle $\alpha$ are givenGiven the Pythagoras Theorem: ${a}^{2}+{b}^{2}={c}^{2}$Is there a way to get the value of b when we only have a value for a and the angle $\alpha$?

Filipinacws 2022-08-12

### Existence of Right Angle in Hilbert AxiomsHilbert, in Foundations of Geometry briefly mentions that the existence of right angles is a corollary to the supplementary angle theorem. (i.e. If two angles are congruent, then their supplementary angles are congruent).How does existence of right angles follow from this?

betterthennewzv 2022-08-11

### Let ABC be an isoscles triangle with $AB=AC$.The bisector of $\mathrm{\angle }B$ meets AC at D.Given that $BC=BD+AD$,we need to figure out $\mathrm{\angle }A$.

tamkieuqf 2022-08-11

### Geometry/trig help - having trouble finding an angle$AB=AC$$AD=BC$$\mathrm{\angle }BAC={20}^{\circ }$Find $\alpha$.

polynnxu 2022-08-10