List of top Mathematics Questions on Geometry

If a line drawn parallel to one side of triangle intersecting the other two sides in distinct points divides the two sides in the same ratio, then it is parallel to third side. State and prove the converse of the above statement.
P is a point on the side BC of $\triangle ABC$ such that $\angle APC = \angle BAC$. Prove that $AC^2 = BC \cdot CP$.
Equation of a plane parallel to the plane \( 9x - 8y + 7z = 10 \) is:
Through which of the following points does the line \[ \frac{x-11}{12} = \frac{y-12}{13} = \frac{z+13}{14} \text{ pass?} \]
If the direction ratios of two parallel lines are 2, 7, 9, then the value of x is:
If the direction ratios of two parallel lines are \( a, b, c \) and \( x, y, z \), then \( az = \dots \)?
If the direction ratios of two mutually perpendicular lines are 5, 2, 4 and 4, 8, x, then the value of x is:
If \( A(2, 3) \) and \( B(4, 5) \) are the end points of a straight line AB, then the slope of straight line AB is:
How many spherical balls can be made out of a solid cube of iron whose edge measures 44 cm and each ball being 4 cm in diameter? (Take \( \pi = \frac{22}{7} \))
In a triangle, if the three angles are in the ratio \( 2 : 5 : 8 \), then the values of those three angles are:
The area of the rectangular park whose length is 7 meters more than its breadth is 260 sq meters. For fencing the entire boundary of the park if ₹9000 is spent, then the cost of fencing per meter is (in ₹):
Among the following, identify the pair of triangles that are NOT similar.
If two planes \( 2x - 4y + 3z = 5 \) and \( x + 2y + \lambda z = 12 \) are mutually perpendicular to each other, then \(\lambda =\):
The angle between two planes \( 2x + y - 2z = 5 \) and \( 3x - 6y - 2z = 7 \) is:
If the line \[ \frac{x - 3}{a} = \frac{y - 4}{b} = \frac{z - 5}{c} \] is parallel to the line \[ \frac{x}{5} = \frac{y}{3} = \frac{z}{2} \] then:
If the line \[ \frac{x - x_1}{a_1} = \frac{y - y_1}{b_1} = \frac{z - z_1}{c_1} \] is parallel to the plane \[ a_2 x + b_2 y + c_2 z + d = 0 \] then:
If \[ \frac{x}{18} = \frac{6}{18} \] then \(x\) is equal to:
The distance of the plane \( x - 2y + 4z = 9 \) from the point \( (2, 1, -1) \) is:
The equation of the plane parallel to the plane \( 3x - 5y + 4z = 11 \) is:
The direction ratios of two straight lines are \( l, m, n \) and \( l_1, m_1, n_1 \). The lines will be perpendicular to each other if:
The direction ratios of a straight line are \( 1, 3, 5 \). Then its direction cosines are:

In the given figure, if $AB = AC$, then prove that $BE = EC$. 

In the figure, \( \triangle ODC \sim \triangle OBA \). If \( \angle BOC = 125^\circ \) and \( \angle CDO = 70^\circ \), then the value of \( \angle OAB \) will be: 

If a line intersects the sides AB and AC at D and E respectively in a triangle ABC and it is parallel to the side BC, then prove that \[ \frac{AD}{AB} = \frac{AE}{AC} \]
In the figure, \( OA, OB, OC, OD \) are drawn such that \( OB = OC \) and \( OA = OD \). Show that \( \angle A = \angle C \) and \( \angle B = \angle D \).