List of top Mathematics Questions on Geometry asked in Maharashtra Class X Board

Out of the following which is a Pythagorean triplet ?
Determine whether the points \( A(1, -3), B(2, -5), C(-4, 7) \) are collinear.
\( \frac{1}{\sin^2 \theta} - \frac{1}{\cos^2 \theta} - \frac{1}{\tan^2 \theta} - \frac{1}{\cot^2 \theta} - \frac{1}{\sec^2 \theta} - \frac{1}{\csc^2 \theta} = -3 \), then find the value of \( \theta \).
A cylinder of radius \( 12 \, \text{cm} \) contains water up to the height \( 20 \, \text{cm} \). A spherical iron ball is dropped into the cylinder, and thus the water level is raised by \( 6.75 \, \text{cm} \). What is the radius of the iron ball?
Find the surface area of a sphere of radius \( 7 \, \text{cm} \).
Find the side of a square whose diagonal is \( 10\sqrt{2} \, \text{cm} \):
$\triangle SHR \sim \triangle SVU$. In $\triangle SHR$, $SH = 4.5$ cm, $HR = 5.2$ cm, and $SR = 5.8$ cm. If $\dfrac{SH}{SV} = \dfrac{3}{5}$, construct $\triangle SVU$.

In trapezium $ABCD$, side $AB \parallel PQ \parallel DC$. If $AP = 3$, $PD = 12$, and $QC = 14$, find $BQ$. 

In $\triangle ABC$, seg $AP$ is a median. If $BC = 18$, and $AB^2 + AC^2 = 260$, find $AP$.