Tag: similarity and right angled triangle

In $\Delta ABC, \, m \angle B = 90$ and $\overline{BM}$ is an altitude. If AB = 2 AM, then AC = ......

P, Q, R are the points of intersection of a line 1 with sides BC, CA, AB of a $\Delta$ ABC 
respectively, then $\dfrac{BP}{PC} \dfrac{CQ}{QA} \dfrac{AR}{RB}$

Sides of triangle are given below. Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse.

The hypotenuse and the semi-perimeter of right triangle are 20 cm and 24 cm, respectively. The other two sides of the triangle are :

In $\Delta PQR,\angle P$ is right angle and $\bar{PM}$ is an altitude. $PQ=\sqrt{20}$ and QM=4 then RM=____.

The lengths of the medians through acute angles of a right-angled triangle are 3 and 4. Find the area of the triangle:

The length of the hypotenuse of an isosceles right triangle whose one side is $4\surd {2}\ cm$  is___________$cm$

Let $ABC$ be a fixed triangle and $P$ be variable point in the plane of a triangle $ABC$. Suppose $a, b, c$ are lengths of sides $BC,  CA,AB$ opposite to angles $A, B, C $ respectively. If $a(PA)^{2} + b(PB)^{2} + c(PC)^{2}$ is minimum, then the point $P$ with respect to $\triangle{ABC}$ is

If $AD,BE$ and $CF$ are the medians of a $\Delta ABC,$ then evaluate  $\displaystyle \left ( AD^{2}+BE^{2}+CF^{2} \right ):\left ( BC^{2}+CA^{2}+AB^{2} \right )=$

The distances of the circumcentre of the acute-angled $  \Delta \mathrm{ABC}  $ from the sides $  \mathrm{BC},  $ CA and AB are in the ratio