In ABC , D is any point on BC . Prove that: AB + BC + AC >2 AD. - Vidyadip

Question

In $\triangle ABC , D$ is any point on BC .
Prove that: $AB + BC + AC >2 AD$.

✓

Answer

[Hint. $A B+B D>A D$ and $A C+C D>A D$.]

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "[3 marks sum]" from Triangles→Triangles — all question types→MATHEMATICS STD 9 question papers→ICSE Board STD 9 question papers→ICSE Board question paper generator→

Similar questions

Two figures are similar. If the ratio of their perimeters is $8:16.$ What will be the ratio of the corresponding sides?

If $x=\frac{1}{5-x}$ and $x \neq 5$ find $x^3+\frac{1}{x^3}$

Find the area of a circle circumscribing an equilateral triangle of side 15 cm. [Take pi = 3.141]

If $\tan A=\frac{1}{2}, \tan B=\frac{1}{3}$ and $\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A \tan B}$, find $A+B$.

Find the area of a circular field that has a circumference of $396\ m.$

Find the length of hypotenuse of an isosceles right angled triangle, having an area of $200 cm^2 .($ Take $\sqrt{2}=1.414)$

PQR is an isosceles triangle inscribed in a circle. If $PQ = PR =25 cm$ and $QR =14 cm$, calculate the radius of the circle to the nearest cm .

In a triangle $ABC.$ If $D$ is a point on $BC$ such that $\angle CAD = \angle B,$ then prove that$: \angle ADC = \angle BAC.$

A number consists of two digits, the difference of whose digits is 3 . If 4 times the number is equal to 7 times the number obtained by reversing the digits, find the number.

Construct a parallelogram $\text{ABCD},$ when$:AB = 6.0 \ cm, AD = 5.0 \ cm$ and $\angle A = 45^\circ .$