Geometry

In $\triangle PQR$, if $\angle P = 50^\circ$ and $\angle R = 50^\circ$, then the triangle is:

The perimeter of a triangle with sides $a, b, c$ is $P$. Which of the following is always true?

In $\triangle ABC$, if $AB = AC$ and $\angle A = 2\angle B$, find $\angle A$.

In $\triangle ABC$, $D$ is the mid-point of $AB$, $E$ is the mid-point of $BC$, and $F$ is the mid-point of $AC$. If $AB=10, BC=12, AC=14$, find the perimeter of parallelogram $ADEF$.

In $\triangle ABC$, mid-points $D, E$ are on $AB, AC$. If $DE$ is parallel to $BC$, then $D$ and $E$:

In $\triangle PQR$, $X$ is the mid-point of $PQ$ and $Y$ is on $PR$ such that $XY \parallel QR$. If $PR = 10.2\text{ cm}$, then $YR$ is:

If the diagonal of a square is $d$, what is the area of the square?

A triangle has sides $8, 15, 17$. What kind of triangle is it?

Find the length of the diagonal of a square whose area is $100\text{ cm}^2$.

Which of the following is a quadrilateral where only one diagonal is bisected by the other?

The consecutive angles of a parallelogram are in the ratio $4:5$. The measure of the larger angle is:

In a rectangle $PQRS$, $\angle OPQ = 30^\circ$ (where $O$ is the intersection of diagonals). The measure of $\angle OQP$ is:

A parallelogram and a triangle are on the same base of $10 cm$ and have the same height of $5 cm$. The difference in their areas is:

In $\Delta ABC$, $D$ is the midpoint of $BC$. If the area of $\Delta ABD$ is $12.5 cm^2$, find the area of $\Delta ABC$.

Parallelogram $ABCD$ has an area of $100 cm^2$. $P$ is the midpoint of the side $CD$. The area of $\Delta ABP$ is:

If the sum of a pair of opposite angles of a quadrilateral is $180^\circ$, the quadrilateral is:

If $O$ is the center of the circle and $\angle AOC = 120^\circ$, then the angle subtended by the major arc $AC$ at the center is:

In a circle, chord $XY$ has length $24$ cm and the radius is $15$ cm. What is the distance of the chord from the center?