List of top Quantitative Aptitude Questions on Geometry

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
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:
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:
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:
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:
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?
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 \(\angle APB\).
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?
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
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:
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 \(\triangle AED\).
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
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
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
If two parallel lines are intersected by a transversal, bisectors of its interior angles will form
Let C be the circle \(x^2+y^2+4x-6y-3=0\) and \(L\) be the locus of the point of intersection of a pair of tangents to \(C\) with the angle between the two tangents equal to \(60º\) . Then, the point at which \(L\) touches the line \(x = 6\) is
In a right-angled triangle Δ ABC , the altitude AB is 5 cm , and the base BC is 12 cm . P and Q are two points on BC such that the areas of ΔABP, ΔABQ , and Δ ABC are in arithmetic progression. If the area of Δ ABC is 1.5 times the area of Δ ABP , the length of PQ , in cm , is
Let \(ΔABC\) be an isosceles triangle such that \(AB\) and \(AC\) are of equal length. \(AD\) is the altitude from \(A\) on \(BC\) and \(BE\) is the altitude from \(B\) on \(AC\) . If \(AD\) and \(BE\) intersect at \(O\) such that \(∠AOB =105\degree\) , then \(\frac{AD}{BE}\) equals
The minor angle between hours hand and minutes hand of a clock was observed at 8:48 am. The minimum deviation (in min) after 8:48 am on when angle increased by 50% is?
In a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is
A quadrilateral \(ABCD\) is inscribed in a circle such that \(AB :CD\) = \(2:1\) and \(BC:AD = 5: 4\). If \(AC\) and \(BD\) intersect at the point \(E\),then \(AE:CE\) equals
 In a regular polygon, each interior angle is 120 more than each exterior angle. Find the number of diagonals of the polygon.
A rectangle with the largest possible area is inscribed in a semi-circle. Find the ratio of the larger side to the smaller side.
In a right-angled triangle Δ ABC , the altitude AB is 5 cm , and the base BC is 12 cm . P and Q are two points on BC such that the areas of ΔABP, ΔABQ , and Δ ABC are in arithmetic progression. If the area of Δ ABC is 1.5 times the area of Δ ABP , the length of PQ , in cm , is
A rectangle with the largest possible area is drawn inside a semicircle of radius 2 cm. Then, the ratio of the lengths of the largest to the smallest side of this rectangle is