Question
In $\triangle\text{ABC, }\angle\text{B}=35^{\circ},\angle\text{C}=65^{\circ}$ and the bisector of $\angle\text{BAC}$ meets $BC$ in $X.$ Arrange $AX, BX$ and $CX$ in descending order.
✓
Answer
Given: in $\triangle\text{ABC, }\angle\text{B}=35^{\circ},\angle\text{C}=65^{\circ}$ and the bisector of $\angle\text{BAC}$ meets $BC$ in $x$ In $\triangle\text{ABX},$
$\because\angle\text{BAX}>\angle\text{ABX}$
$\therefore\text{BX}>\text{AX}...(\text{i})$
$\therefore\text{AX}>\text{CX}...(\text{ii})$ From $(i)$ and $(ii),$ we get $\text{BX > AX > CX}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If the complement of an angle is equal to the supplement of the thrice of it. Find the measure of the angle.
Form the frequency distribution table and Find the mean of the marks obtained by $30$ students of Class $IX$ of a school, as given below:
$10, 20, 36, 92, 95, 40, 50, 56, 60, 70, 92, 88, 80, 70, 72, 70, 36, 40, 36, 40, 92, 40, 50, 50, 56, 60, 70, 60, 60, 88$
→$10, 20, 36, 92, 95, 40, 50, 56, 60, 70, 92, 88, 80, 70, 72, 70, 36, 40, 36, 40, 92, 40, 50, 50, 56, 60, 70, 60, 60, 88$
Using the remainder theorem, find the remainder, when $p(x)$ is divided by $g(x)$, where, $p(x) = x^3 - ax^2 + 6x - a, g(x) x - a.$
→A traffic signal board, indicating $\text{SCHOOLAHEAD}$ is an equilateral triangle with side a Find the area of the signal board, using Heron's formula. If its perimeter is $180 \ cm$, what will be the area of the signal board?
→Using the remainder theorem, find the remainder, when $p(x)$ is divided by $g(x)$, where, $p(x) = x^3 - 6x^2 + 2x - 4$, $\text{g}(\text{x})=1-\frac{3}{2}\text{x}.$
→Factorise: $\frac{1}{3}\text{x}^2-2\text{x}-9$
→Show that the bisectors of angles of a parallelogram form a rectangle.
Evaluate the following:$ (99)^3$
→Determine which of the following polynomials has $x - 2$ a factor:
$i. 3x^2 + 6x - 24$
$ii. 4x^2+ x – 2$
→$i. 3x^2 + 6x - 24$
$ii. 4x^2+ x – 2$
The diameter of the moon is approximately one-fourth of the diameter of the earth. What is the earth the volume of the moon?