# Angle Bisectors Problems: Solutions & Examples

Recent questions in Angle Bisectors
Kole Meyers 2023-03-11

## The angles of a triangle are in the ratio 1 : 1 : 2. What is the largest angle in the triangle? $A\right){90}^{\circ }\phantom{\rule{0ex}{0ex}}B\right){135}^{\circ }\phantom{\rule{0ex}{0ex}}C\right){45}^{\circ }\phantom{\rule{0ex}{0ex}}D\right){150}^{\circ }$

Shayla Phelps 2023-03-05

## How many right angles are required to create a complete angle?1) Two2) Three3) Four4) Five

Bridger Joyce 2023-02-28

## How can I find an equation for the perpendicular bisector of the line segment that has the endpoints , (9,7) and (−3,−5)?

reiselivloy 2023-02-11

## What angle is a $1$ in $10$ slope?

ikalawangq00 2023-02-08

## An angle formed by two opposite rays is called : Zero angle Complete angle Right angle Straight angle

Isaias Black 2023-01-22

## Show that each diagonal of a rhombus bisects the angle through which it passes: ?

animeagan0o8 2023-01-21

## Find the central angle θ which forms a sector area 18 square feet of a circle of a radius of 10 feet?

Isaias Black 2022-12-27

## What value of y would make AOB, a line in the figure, if ∠AOC=4y and ∠BOC=(6y+30).

vegetatzz8s 2022-11-25

## Is it true that A ray is a bisector of an angle if and only if it splits the angle into two angles?

Kareem Mejia 2022-11-17

## Just like we have it in 2D coordinate geometry, is there an equation which describes the angle bisector of two straight lines in 3D coordinate geometry?

vedentst9i 2022-11-14

## Compute the coordinate equation of the angle bisectors of the planes E and F.$E:x+4y+8z+50=0$ and $F:3x+4y+12z+82=0$Proceed as follows:a) Find the normal vectors of the two angle-bisecting planes.b) Find a shablack point of planes E and F.c) Now determine the equations of the two angle-bisecting planes.I have the solutions but I don't understand why I must do things the way the solution is shown.$|\left(\begin{array}{c}3\\ 4\\ 12\end{array}\right)|=13$are the normal vectors from the equations. But this is not a good enough answer, all they asked for is the normal vectors, aren't these the normal vectors? Why must I add and subtract them like this?:$13\cdot \left(\begin{array}{c}1\\ 4\\ 8\end{array}\right)+9\cdot \left(\begin{array}{c}3\\ 4\\ 12\end{array}\right)$$13\cdot \left(\begin{array}{c}1\\ 4\\ 8\end{array}\right)-9\cdot \left(\begin{array}{c}3\\ 4\\ 12\end{array}\right)$b) The solution says that I must choose one component, e.g: $x=2$ and then I substitute it into the equations and complete the simultaneous equation to find the point. Must it be only the x component? And why the value 2? Can it be any value? So according to the solution, the shablack point is $P\left(2,5,-9\right)$c) The solution uses the answers from part a and b and gets this$\left(\begin{array}{c}10\\ 22\\ 53\end{array}\right)\cdot \left[\left(\begin{array}{c}x\\ y\\ z\end{array}\right)-\left(\begin{array}{c}2\\ 5\\ -9\end{array}\right)\right]$$\left(\begin{array}{c}-7\\ 8\\ -2\end{array}\right)\cdot \left[\left(\begin{array}{c}x\\ y\\ z\end{array}\right)-\left(\begin{array}{c}2\\ 5\\ -9\end{array}\right)\right]$Is it a general rule to use the normal to find the equation from a shablack point?

Brenda Jordan 2022-11-08

## The ratios of the lengths of the sides $BC$ and $AC$ of a triangle $ABC$ to the radius of the circumscribed circle are equal to 2 and $\frac{3}{2}$ respectively.Find the ratio of the lengths of the bisectors of internal angles of $B$ and $C$.We are given $\frac{BC}{R}=\frac{a}{R}=2$ and $\frac{AC}{R}=\frac{b}{R}=\frac{3}{2}$,where $R$ is the circumradius of the triangle $ABC$.$a=2R,b=\frac{3}{2}R$I know that ${m}_{b}$=length of angle bisector of angle $B=\frac{2\sqrt{acs\left(s-b\right)}}{a+c}$ and ${m}_{c}$=length of angle bisector of angle $C=\frac{2\sqrt{abs\left(s-c\right)}}{a+b}$ but i need the third side in order to use these formulae,which i do not know.What should i do?

Widersinnby7 2022-11-03

## The angle bisector of${L}_{1}:{a}_{1}x+{b}_{1}y+{c}_{1}=0$and${L}_{2}:{a}_{2}x+{b}_{2}y+{c}_{2}=0$$\left({a}_{i},{b}_{i},{c}_{i}\right)\in \mathbb{R}$can be found be solving the equation But our teacher told us that the equation of the angle bisector pasing through the region containing the origin can be obtained by solving only the positive case of the equation given that $\left({c}_{1},{c}_{2}\right)>0$.How can we prove this?

Aldo Ashley 2022-10-22

## The lengths of segments $PQ$ and $PR$ are 8 inches and 5 inches, respectively, and they make a 60-degree angle at P. Find the length of the angle bisector of angle R.Through the Law of Sines I was able to find that the angle measure of R is approximately ${81.787}^{\circ }$ and from the Law of Cosines I figublack out that the measure of side $QR$ is 7 inches.I am unsure of what steps I should take to find the measure of the angle bisector. Any help will be greatly appreciated!

snaketao0g 2022-10-20

## How can I find a relation describing the length of angle bisector of regular polygon expressed as a function of its side's length?For a equilateral triangle and a square with a side of length a, the relations are:${t}_{a}=\frac{a\sqrt{3}}{2}$and${t}_{a}=\frac{a\sqrt{2}}{2}$Could this be generalised to relation describing bisector's length of a regular N− polygon?

c0nman56 2022-10-20

## I have seen in an old geometry textbook that the formula for the length of the angle bisector at $A$ in $\mathrm{△}\mathit{A}\mathit{B}\mathit{C}$ is${m}_{a}=\sqrt{bc\left[1-{\left(\frac{a}{b+c}\right)}^{2}\right]},$and I have seen in a much older geometry textbook that the formula for the length of the same angle bisector is${m}_{a}=\frac{2}{b+c}\sqrt{bcs\left(s-a\right)}.$(s denotes the semiperimeter of the triangle.)I did not see such formulas in Euclid's Elements. Was either formula discoveblack by the ancient Greeks? May someone furnish a demonstration of either of them without using Stewart's Theorem and without using the Inscribed Angle Theorem?

Chaim Ferguson 2022-10-16