Question
In a $\triangle\text{ABC,D}\ \text{and E}$ are points on the sides AB and AC respectively such that DE || BC.
If AD = 8cm, AB = 12cm and AE = 12cm, find CE.
If AD = 8cm, AB = 12cm and AE = 12cm, find CE.
✓
Answer
AD = 8cm, AB = 12cm, AE = 12cm
DB = AB - AD
DB = 12 - 8
DB = 4cm
by thales theorem,
$\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}$
$\Rightarrow\frac{8}{4}=\frac{12}{\text{EC}}$
$\Rightarrow\text{EC}=\frac{12\times4}{8}$
$\Rightarrow\text{EC}=6\text{cm}$
DB = AB - AD
DB = 12 - 8
DB = 4cm
by thales theorem,
$\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}$
$\Rightarrow\frac{8}{4}=\frac{12}{\text{EC}}$
$\Rightarrow\text{EC}=\frac{12\times4}{8}$
$\Rightarrow\text{EC}=6\text{cm}$
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
Is $0$ a term of the A.P:$ 31, 28, 25, 25, ........? $Justify your answer.
→Find the area of a shaded region in the the following figure,where a circular arc of radius $7\ cm$ has been drawn with vertex A of an equilateral triangle $ABC$ of side $14\ cm$ as centre. $\big(\text{Use }\pi=\frac{22}{7}$ and $\sqrt{3}=1.73\big)$
→In the AP, 38, ? , ? , ? , –22, find the missing terms?
In $\triangle\text{ABC},$ if $\text{BD}\perp\text{AC}$ and $BC^2 = 2AC \times CD$, then prove that $AB = AC.$
→In the given figure, $\triangle\text{ABC}$ is right angled at C and $\text{DE}\perp\text{AB.}$ Prove that $\triangle\text{ABC}\sim\triangle\text{ADE}$ and hence find the length of AE and DE.
→Prove the following.
$(\sin\alpha+\cos\alpha)(\tan\alpha+\cot\alpha)=\sec\alpha+\text{cosec}\alpha$
→$(\sin\alpha+\cos\alpha)(\tan\alpha+\cot\alpha)=\sec\alpha+\text{cosec}\alpha$
Find the sum of first 16 terms of the A.P. whose $n ^{\text {th }}$ term is given by $a _{ n }=5 n -3$.
→Two men on either side of the cliff 80m high observes the angles of a elevation of the top of the cliff to be 30° and 60° respectively. Find the distance between the two men.
Two number differ by $3$ and their product is $504$. Find the numbers.
→Prove the following trigonometric identities.
$\frac{1}{1+\sin\text{A}}+\frac{1}{1-\sin\text{A}}=2\sec^2\text{A}$
→$\frac{1}{1+\sin\text{A}}+\frac{1}{1-\sin\text{A}}=2\sec^2\text{A}$