Introduction to Geometry

The number of points a line can have been:

The sides of a quadrilateral are extended to make the angles as shown below.


What is the value x?

In a trapezium $\mathrm{ABCD},\mathrm{AB}\parallel \mathrm{CD}$ and the diagonals meet at point $\mathrm{O}$. If $\mathrm{AB}=6 \mathrm{cm}$ and $\mathrm{DC}=3 \mathrm{cm}$, then the ratio of $\mathrm{ar}(△\mathrm{AOB})$ and $\mathrm{ar}(△\mathrm{COD})$ will be ____ .

$\mathrm{ABCD}$ is a square. $\mathrm{M}$ is the mid-point of $\mathrm{AB}$ and $\mathrm{N}$ is the mid-point of $\mathrm{BC}$. $\mathrm{DM}$ and $\mathrm{AN}$ are joined and they meet at $\mathrm{O}$. Then which of the following is not correct?

In $∆ABC$, $AB=5 \mathrm{cm}$,  $AC=7 \mathrm{cm}$. If $AD$ is the angle bisector of $\angle A$, then $BD : CD$ is-

$∆ABC$ is an isosceles triangle with $AB=AC$. A circle through $B$ touching $AC$ at the middle point Intersects $AB$ at $P$. Find $AP:AB$ is:

A polygon has $54$ diagonals. Find the number of sides in the polygon$?$

The area of an equilateral triangle is $4\sqrt{3} {\mathrm{cm}}^2$. The length of each side of the triangle is:

If points$A (1, – 1), B (5, 2) and C (9, 5)$are collinear, then which option is correct?

If the area of an equilateral triangle is $24\sqrt{3} {\mathrm{cm}}^2$. Then its perimeter is -

In quadrilateral $PQRS$, name:

Two points which are exterior of the quadrilateral.

$AB$ is a chord of a circle with centre $O$ and $P$ is any point on the circle. If $\angle APB = 122°$, then what is the measure of $\angle OAB$?

Two circles of radius $15 \mathrm{cm}$ and $37 \mathrm{cm}$ intersect each other at points $A$ and $B$. If the length of the common chord is $24 \mathrm{cm}$, what is the distance (in $\mathrm{cm}$) between the centres of the circles?

In the given figure, the value of $m$ is

In a circle with centre $O$ and radius $13 \mathrm{cm}$, a chord $AB$ is drawn. Tangents at $A$ and $B$ intersects at $P$ such that $\angle APB = 60°$. If the distance of $AB$ from the centre $O$ is $5 \mathrm{cm}$, then what is the length (in $\mathrm{cm}$) of $AP$?

$ABCD$ is a cyclic quadrilateral. $AB$ and $DC$ meet at $F$, when produced. $AD$ and $BC$ meet at $E$, when produced. If $\angle BAD = 68°$ and $\angle AEB = 27°$, then what is the measure of $\angle BFC$?

A chord $AB$ of circle $C_1$ of radius $17 \mathrm{cm}$ touches circle $C_2$ which is concentric to $C_1$. The radius of $C_2$ is $8 \mathrm{cm}$. What is the length (in $\mathrm{cm}$) of $AB$?

$ABCD$ is a cyclic quadrilateral such that $AB$ is the diameter of the circle and $\angle ADC = 145°$, then what is the measure of $\angle BAC$?

A $\Delta ABC$ has sides $5 \mathrm{cm}, 6 \mathrm{cm}$ and $7 \mathrm{cm}$. $AB$ extended touches a circle at $P$ and $AC$ extended touches the same circle at $Q$. Find the length (in $\mathrm{cm}$) of $AQ$.

If a triangle $ABC$ is right- Triangle at $A$, then what is the value of $\sin \frac{B+C}{2}\cos \frac{B+C}{2}$?