Recent questions tagged geometry

If $\left (-4, 0 \right), \left(1, -1 \right)$ are two vertices of a triangle whose area is $4$ Sq units then its third vertex lies on :$y=x$$5x+y+12=0$$x+5y-4=0$$x-5y+4=...

In a triangle $XYZ$, $P$ and $Q$ are points on ${XY,XZ}$ respectively such that $XP=2PY$, $XQ=2QZ$, then the ratio, of area of $\triangle XPQ$ and area of $\triangle XYZ$...

A conical tent is to accommodate $10$ persons. Each person must have $6m^{2}$ space to sit and $30m^{3}$ of air to breath. What will be height of cone?$37.5$ m$150$ m$75$...

In a bangle shop. If the shopkeeper displays the bangles in the form of a square then he is left with $38$ bangles. If he wanted to increase the size of square by one ban...

A cylindrical box of radius $5$ cm contains $10$ solid spherical balls each of radius $5$ cm. If the topmost ball touches the upper cover of the box, then the volume of t...

If $(-4,0),(1,-1)$ are two vertices of a triangle whose area is $4$ Sq units then its third vertex lies on:$y=x$$5x+y+12=0$$x+5y-4=0$$x-5y+4=0$

For a sphere of radius $10$ cm, the numerical value of the surface area is how many percent of the numerical value of its volume?$26.5\%$$24\%$$30\%$$45\%$

Line $AB$ is $24$ metres in length and is tangent to the inner one of the two concentric circles at point $C.$ Points $A$ and $B$ lie on the circumference of the outer ci...

If $10$, $12$ and '$x$' are sides of an acute angled triangle, how many integer values of '$x$' are possible?$7$$12$$9$$13$

The length of a rope, to which a cow is tied, is increased from $19$ m to $30$ m. How much additional ground will it be able to graze ? Assume that the cow is able to mov...

What is the measure of the radius of the circle that circumscribes a triangle whose sides measure $9, 40$ and $41$?$6$$4$$24.5$$20.5$

Two circles, each of radius $4$ cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, the...

In a triangle $\text{ABC}$, medians $\text{AD}$ and $\text{BE}$ are perpendicular to each other, and have lengths $12$ cm and $9$ cm, respectively. Then, the area of tria...

Let $\text{A}$ and $\text{B}$ be two regular polygons having $\text{A}$ and $\text{B}$ sides, respectively. If $b= 2a$ and each interior angle of $\text{B}$ is $3/2$ time...

Let $\text{ABC}$ be a right-angled triangle with hypotenuse $\text{BC}$ of length $20$ cm. If $\text{AP}$ is perpendicular on $\text{BC}$, then the maximum possible lengt...

On a triangle $\text{ABC}$, a circle with diameter $\text{BC}$ is drawn, intersecting $\text{AB}$ and $\text{AC}$ at points $\text{P}$ and $\text{Q}$, respectively. If th...

A parallelogram $\text{ABCD}$ has area $48$ sqcm. If the length of $\text{CD}$ is $8$ cm and that of $\text{AD}$ is $s$ cm, then which one of the following is necessarily...

From a rectangle $\text{ABCD}$ of area $768$ sq cm, a semicircular part with diameter $\text{AB}$ and area $72\pi$ sq cm is removed. The perimeter of the leftover portion...

The area of a rectangle and the square of its perimeter are in the ratio $1:25$. Then the lengths of the shorter and longer sides of the rectangle are in the ratio$1:4$$2...

In a circle, two parallel chords on the same side of a diameter have lengths $4$ cm and $6$ cm. If the distance between these chords is $1$ cm, then the radius of the cir...

Given an equilateral triangle $\text{T1}$ with side $24$ cm, a second triangle $\text{T2}$ is formed by joining the midpoints of the sides of $\text{T1}$. Then a third tr...

In a circle with center $\text{O}$ and radius $1$ cm, an arc $\text{AB}$ makes an angle $60$ degrees at $\text{O}$. Let $\text{R}$ be the region bounded by the radii $\te...

Let $\text{ABCD}$ be a rectangle inscribed in a circle of radius $13$ cm. Which one of the following pairs can represent, in cm, the possible length and breadth of $\text...

In a parallelogram $\text{ABCD}$ of area $72$ sq cm, the sides $\text{CD}$ and $\text{AD}$ have lengths $9$ cm and $16$ cm, respectively. Let $\text{P}$ be a point on $\t...

$\text{ABCD}$ is a quadrilateral inscribed in a circle with centre $\text{O}$. If $\angle \text{COD} =120$ degrees and $\angle \text{BAC} = 30$ degrees, then the value of...

The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths $10$ cm and $20$ cm while the other two sides are of equal len...

Let $\text{ABCDEF}$ be a regular hexagon with each side of length $1$ cm. The area (in sq cm) of a square with $\text{AC}$ as one side is $3\sqrt{2}$$3$$4$$\sqrt{3}$

Let $\text{P}$ be an interior point of a right-angled isosceles triangle $\text{ABC}$ with hypotenuse $\text{AB}$. If the perpendicular distance of $\text{P}$ from each o...

If three sides of a rectangular park have a total length $400$ ft, then the area of the park is maximum when the length (in ft) of its longer side is$299$$200$$201$$399$

Let $\text{ABC}$ be a right-angled triangle with $\text{BC}$ as the hypotenuse. Lengths of $\text{AB}$ and $\text{AC}$ are $15$ km and $20$ km, respectively. The minimum ...

Let $\text{ABC}$ be a right-angled isosceles triangle with hypotenuse $\text{BC}$. Let $\text{BQC}$ be a semi-circle, away from A, with diameter $\text{BC}$. Let $\text{B...

Let $\text{AB, CD, EF, GH}$, and $\text{JK}$ be five diameters of a circle with center at $\text{O}$. In how many ways can three points be chosen out of $\text{A, B, C, D...

If $\text{ABCD}$ is a square and $\text{BCE}$ is an equilateral triangle, what is the measure of $\angle \text{DEC}?$$15^{\circ}$$30^{\circ}$$20^{\circ}$$45^{\circ}$