List of top Quantitative Aptitude Questions on Geometry

The $(x, y)$ coordinates of vertices $P$, $Q$ and $R$ of a parallelogram $PQRS$ are $(-3, -2)$, $(1, -5)$ and $(9, 1)$, respectively. If the diagonal $SQ$ intersects the x-axis at $(a, 0)$, then the value of $a$ is:
In a circle with center $C$ and radius $6\sqrt{2}$ cm, $PQ$ and $SR$ are two parallel chords separated by one of the diameters. If $\angle PQC = 45^\circ$, and the ratio of the perpendicular distance of $PQ$ and $SR$ from $C$ is $3:2$, then the area, in sq. cm, of the quadrilateral $PQRS$ is:
In $\Delta ABC$, $AB = AC = 12 \text{ cm}$ and $D$ is a point on side $BC$ such that $AD = 8 \text{ cm}$. If $AD$ is extended to a point $E$ such that $\angle ACB = \angle AEB$, then the length, in cm, of $AE$ is
Two circles of radii 6 cm and 6 cm intersect each other. The distance between their centers is 8 cm. What is the length of their common chord?
In a $\triangle ABC$, points $D$ and $E$ are on the sides $BC$ and $AC$, respectively. $BE$ and $AD$ intersect at point $T$ such that $AD : AT = 4 : 3$, and $BE : BT = 5 : 4$. Point $F$ lies on $AC$ such that $DF$ is parallel to $BE$. Then, $BD : CD$ is:
In a triangle ABC, the sides are in the ratio 3 : 4 : 5. If the area of the triangle is 96 sq units, what is its perimeter?
If the length of a side of a rhombus is 36 cm and the area of the rhombus is 396 sq. cm, then the absolute value of the difference between the lengths, in cm, of the diagonals of the rhombus is:
Two tangents drawn from a point $P$ touch a circle with center $O$ at points $Q$ and $R$. Points $A$ and $B$ lie on $PQ$ and $PR$, respectively, such that $AB$ is also a tangent to the same circle. If $\angle AOB = 50^{\circ}$, then $\angle APB$, in degrees, equals:
From an external point P, two tangents PA and PB are drawn to a circle with centre O. Radii OA and OB are perpendicular to the tangents and the angle \(\angle AOB = 50^\circ\). A third tangent is drawn which intersects both PA and PB. Find the angle \(\angle APB\).
A triangle $ABC$ is formed with $AB = AC = 50 \text{ cm}$ and $BC = 80 \text{ cm}$. Then, the sum of the lengths, in cm, of all three altitudes of the triangle $ABC$ is
In triangle ABC, AB = 6 cm, AC = BC = 7 cm. Also, CP is a median. Which of the following is the area of triangle ABC?
triangle ABC, AB = 6 cm, AC = BC = 7 cm.
ABC and PQR are 2 identical equilateral triangles overlapping each other.
The area of the overlapping region PXBY is equal to twice the area of triangle AXP.
2 identical equilateral triangles overlapping each other.
If the sum of the interior angles of a polygon is \(1260^\circ\), how many sides does it have?
What is the sum of interior angles of a polygon with 10 sides?
In the $XY$-plane, the area, in sq. units, of the region defined by the inequalities $y \ge x + 4$ and $-4 \le x^2 + y^2 + 4(x - y) \le 0$ is
Three circles of equal radii touch (but not cross) each other externally. Two other circles, X and Y, are drawn such that both touch (but not cross) each of the three previous circles. If the radius of X is more than that of Y, the ratio of the radii of X and Y is
A rectangle \(ABCD\) has sides \(AB = 45 \, \text{cm}\) and \(BC = 26 \, \text{cm}\). Point \(E\) is the midpoint of side \(CD\). Find the radius of the incircle of the triangle \(\triangle AED\).
The coordinates of the three vertices of a triangle are: (1, 2), (7, 2), and (1, 10). Then the radius of the incircle of the triangle is
If two parallel lines are intersected by a transversal, bisectors of its interior angles will form
In the xy-plane, if line k has negative slope and passes through the point (-5,r), is the x-intercept of line k positive?
(1) The slope of line k is -5.
(2) r > 0
A closed cylindrical tank contains 36\(\pi\) cubic feet of water and is filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of the water in the tank is 4 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?
In the diagram above, triangle PQR has a right angle at Q. If PQ>QR, then what is the ratio of the area of triangle PQS to the area of triangle RQS?
I. Line segment QS is perpendicular to PR and has a length of 12.
II. PQR has a perimeter of 60.
The figure above represents a picture set in a square wooden frame that is "p" inches wide on all sides. If the combined area of picture and the frame is equal to "q" square inches, then in terms of p and q, what is the perimeter of the picture?
If p is the perimeter of rectangle Q, what is the value of p?
(1) Each diagonal of rectangle Q has length 10.
(2) The area of rectangle Q is 48.
If X and Y are points in a plane and X lies inside the circle C with center O and radius 2, does Y lie inside circle C?
(1) The length of line segment XY is 3.
(2) The length of line segment OY is 1.5.