Recent questions tagged geometry

Let $\triangle A B C$ be an isosceles triangle such that $A B$ and $A C$ are of equal length. $A D$ is the altitude from $A$ on $B C$ and $B E$ is the altitude from $B$ o...

A rectangle with the largest possible area is drawn inside a semicircle of radius $2 \mathrm{~cm}$. Then, the ratio of the lengths of the largest to the smallest side of ...

In a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is

Let $\triangle A B C$ be an isosceles triangle such that $A B$ and $A C$ are of equal length. $A D$ is the altitude from $A$ on $B C$ and $B E$ is the altitude from $B$ o...

A rectangle with the largest possible area is drawn inside a semicircle of radius $2 \mathrm{~cm}$. Then, the ratio of the lengths of the largest to the smallest side of ...

In a regular polygon, any interior angle exceeds the exterior angle by $120$ degrees. Then, the number of diagonals of this polygon is

In a rectangle $A B C D, A B=9 \mathrm{~cm}$ and $B C=6 \mathrm{~cm}$. $P$ and $Q$ are two points on $B C$ such that the areas of the figures $A B P, A P Q$, and $A Q C D...

A triangle is drawn with its vertices on the circle $C$ such that one of its sides is a diameter of $C$ and the other two sides have their lengths in the ratio $a: b$. If...

The area of the quadrilateral bounded by the $Y$-axis, the line $x=5$, and the lines $|x-y|-|x-5|=2$, is

A quadrilateral $A B C D$ is inscribed in a circle such that $A B: C D=2: 1$ and $B C: A D=5: 4$. If $A C$ and $B D$ intersect at the point $E$, then $A E: C E$ equals$2:...

In a right-angled triangle $\triangle A B C$, the altitude $A B$ is $5 \mathrm{~cm}$, and the base $B C$ is $12 \mathrm{~cm} . P$ and $Q$ are two points on $B C$ such tha...

The vertices of a triangle are $(0,0), (4,0)$ and $(3,9).$ The area of the circle passing through these three points is $\frac{14 \pi}{3}$$\frac{12 \pi}{5}$$\frac{123 \pi...

The points $(2,1)$ and $( – 3, – 4)$ are opposite vertices of a parallelogram. If the other two vertices lie on the line $x + 9y + c = 0,$ then $\text{c}$ is $12$$14$$13$...

In a trapezium $\text{ABCD},\; \text{AB}$ is parallel to $\text{DC}, \; \text{BC}$ is perpendicular to $\text{DC}$ and $\angle \text{BAD} = 45^{\circ}.$ If $\text{DC} = 5...