MCQ
In a $\triangle\text{ABC}$ it is given that AD is the internal bisector of $\angle\text{A}.$ If BD = 4cm, DC = 5cm and AB = 6cm, then AC =?
- A4.5cm
- B8cm
- C9cm
- ✓7.5cm
✓
Answer
Correct option: D.
7.5cm
since AD is the bisector of $\angle\text{A},$
by the angle bisector theorem,
$\frac{\text{AB}}{\text{AC}}=\frac{\text{BD}}{\text{DC}}$
$\Rightarrow\frac{6}{\text{x}}=\frac{4}{5}$
$\Rightarrow\text{x}=7.5\text{cm}$
So, AC = 7.5cm.
by the angle bisector theorem,
$\frac{\text{AB}}{\text{AC}}=\frac{\text{BD}}{\text{DC}}$
$\Rightarrow\frac{6}{\text{x}}=\frac{4}{5}$
$\Rightarrow\text{x}=7.5\text{cm}$
So, AC = 7.5cm.
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
The area of the circle that can be inscribed in a square of side $6 cm$ is
→The value of $k$ for which the system of equations $x + y - 4 = 0$ and $2x + ky = 3$ has no solution, is :
→In the figure $,PQ$ and $PR$ are two tangents to a circle with centre $O$. If $\angle\text{QPR}=46^\circ$ then $\angle\text{QOR}$ equals :
→In a $\triangle ABC , \angle A =x^{\circ}, \angle B =(3 x-2)^{\circ}, \angle C =y^{\circ}$. Also $\angle C -\angle B =9^{\circ}$. The sum of the greatest and the smallest angles of this triangle is
→How many tangents can be drawn to a circle from a point on it?
The roots of the quadratic equation $\frac{11}{3+x}=4(3-x)$ are
→If the equation $x^2+ 6(k + 2)x + 9k = 0$ has equal roots then $k = ?$
→The distance of the point $(4, 7)$ from the $y-$ axis is :
→In $\triangle\text{ABC}\angle\text{BAC}=90^\circ$ and $\text{AD} \bot\text{BC}$ then :
→In a $\triangle\text{ABC}$ it is given that $AD$ is the internal bisector of $\angle\text{A}.$ If $BD = 4\ cm, DC = 5\ cm$ and $AB = 6\ cm,$ then $AC =?$
→