SSC CGL QUANT QUIZ(GEOMETRY)

The length of the altitudes of a triangle are $12 \mathrm{~cm}, 15 \mathrm{~cm}$ and $20 \mathrm{~cm}$ respectively. Find Inradius of the triangle.

Given that $\triangle \mathrm{DEF} \sim \triangle \mathrm{ABC}$. If the area of $\triangle \mathrm{ABC}$ is $9 \mathrm{~cm}^{2}$ and that of $\triangle \mathrm{DEF}=12 \mathrm{~cm}^{2}$ and $\mathrm{BC}$ $=2.1 \mathrm{~cm}$, then the length of $\mathrm{EF}$ is:

In $\triangle \mathrm{ABC}, \angle \mathrm{BAC}=90^{\circ}$ and $\mathrm{AD} \perp \mathrm{BC} .$ If $\mathrm{BD}=$ $4 \mathrm{~cm}$ and $\mathrm{CD}=9 \mathrm{~cm}$, then the length of the $\mathrm{AD}(\mathrm{in} \mathrm{cm})$ is?

If two equal circles of radius $7 \mathrm{~cm}$ have two common tangent $A B$ and $C D$ which touch the circles on $A, C$ and $B, D$ respectively and if $\mathrm{CD}=48 \mathrm{~cm}$. Find the length of $\mathrm{AB}$ ?

Two tangents PA and PB are drawn from an external point P to a circle with centre $\mathrm{O}$ at the points $\mathrm{A}$ and $\mathrm{B}$ respectively on it, such that $\angle A P B=60^{\circ}$ and $\mathrm{AP}=16 \sqrt{3} \mathrm{~cm}$. What is the radius of the circle $($ in $\mathrm{cm})$ ?

In the figure, a circle touches all the four sides of a quadrilateral $A B C D$ whose sides $A B=12.6 \mathrm{~cm}$, $A D=11.8 \mathrm{~cm}$ and $C D=8.9 \mathrm{~cm}$. The length of $B C$ (in $\mathrm{cm}$ ) is:

In a circle with centre $\mathrm{O}, \mathrm{PR}$ and $\mathrm{QS}$ meet at the point $\mathrm{T}$, when produced, and $\mathrm{PQ}$ is a diameter. If $\angle R O S=42^{\circ}$, then the measure of $\angle P T Q$ is :