Triangles

If $O$ is the in-centre of $∆\mathrm{ABC}$ and if $\angle BOC=120°$, then find the measure of $\angle BAC$.

If in the triangles $ABC$ and $EDF$, $\angle A$ is equal to $\angle E$, both are equal to $40°$, $AB:ED=AC:EF$ and $\angle F$ is $65°$, then angle $B$ is:

If one angle is the sum of the other two angles and the difference between the greatest and least angles is $60°$, then the formed triangle is called _____.

If $S$ is the circumcentre of $∆\mathrm{ABC}$ and $\angle A=50°$, then find the value of $\angle BCS$.

If each angle of triangle is in the ratio of $2:3:5$, then find the largest angle of triangle.

An isosceles triangle ABC is right-angled at B. D is a point inside the triangle ABC. P and Q are the feet of the perpendiculars drawn from D on the sides AB and AC respectively of triangle ABC. If$AP=a \mathrm{cm}, AQ=b \mathrm{cm}$and $\angle BAD=15°, \sin 75° =$ _____.

$I$ is the incentre of a $∆ABC$. If $\angle ABC=65°$ and $\angle ACB=55°$, then the value of $\angle BIC$ is:

In a $∆ABC$, $\angle B=60°$, $\angle C=40°$ and $AD$ and $AE$ are respectively the bisector of $\angle A$ and the perpendicular drawn to $BC$. The $\angle EAD$ is:

In $\mathrm{\Delta ABC}$, the medians $\mathrm{AD}, \mathrm{BE} \& \mathrm{CF}$ intersect each other at the point $\mathrm{G}$. If the area of $\mathrm{\Delta ABC}$ is $36 {\mathrm{cm}}^2$, then the area (in sq. cm) of the quadrilateral $\mathrm{BDGF}$  is ______

In the above figure, what is the value of  $\mathrm{x}$?

$O$ is the orthocentre of a $∆ABC$. If $\angle BOC=110°$, $\angle BAC$ is equal to:

Let $∆\mathrm{ABC}$ be an equilateral triangle. Let $BE\perp CA$ meeting $CA$ at $E$, then find the value of $(A{B}^2 +B{C}^2 +C{A}^2)$.

If $∆\mathrm{ABC}$ is an equilateral triangle and $D$ is a point on $BC$ such that $AD\perp BC$, then find the ratio of $AB : BD$.

If triangle $ABC$ is similar to triangle $DEF$ such that $BC=3 \mathrm{cm}$, $EF=4 \mathrm{cm}$ and area of triangle $ABC=54 {\mathrm{cm}}^2$, then the area of triangle $DEF$ is:

In $∆\mathrm{ABC}$, BD and CE are perpendicular to AC and AB respectively. If BD = CE, then$∆\mathrm{ABC}$is_____.

The circumcentre of an obtuse triangle will always be in the _____.

The largest and the second largest angles of a triangle are in the ratio of $13:12$ respectively. The smallest angle is $20\%$ of the sum of the largest and the second largest angles. What is the sum of the smallest and the second largest angles?

The triangle $△\mathrm{ABC}$ and $△\mathrm{DEF}$ are similar and the areas are respectively $81 {\mathrm{cm}}^2$ and $196 {\mathrm{cm}}^2$. If $EF = 19.6 \mathrm{cm}$ then find the length of the side $BC$.

In $∆ABC$, $D$ and $E$ point in such that $DE\parallel BC$ and $AD:BD=2:3$, then find the ratio of the area of parallelogram $DECB$ and $∆ABC$:

Find the area of the triangle formed by the graph of $\mathrm{ax} + \mathrm{by} = \mathrm{c}$ (Where a, b are positive real numbers) ?