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Question 1:

The perimeters of two similar triangles $\Delta \mathrm{ABC}$ and $\Delta \mathrm{PQR}$ are $36 \mathrm{~cm}$ and $24 \mathrm{~cm}$ respectively. If $\mathrm{PQ}=10 \mathrm{~cm}$, then $\mathrm{AB}$ is:

Question 2:

PQRS is a rectangle. The ratio of the sides PQ and $Q R$ is $4: 3$. If the length of the diagonal $\mathrm{PR}$ is $20 \mathrm{~cm}$, then what is the area (in $\mathrm{cm}^{2}$ ) of the rectangle?

Question 3:

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?

Question 4:

In a quadrilateral $A B C D, \angle C=102^{\circ}$ and $\angle D=58^{\circ}$. The bisectors of $\angle A$ and $\angle B$ meet at $\mathrm{P}$. What is the measure of $\angle A \mathrm{~PB}$ ?

Question 5:

In $\triangle A B C$, the sides $\mathrm{AB}$ and $\mathrm{AC}$ are produced to $\mathrm{P}$ and $\mathrm{Q}$, respectively. The bisectors of $\angle \mathrm{PBC}$ and $\angle \mathrm{QCB}$ intersect at a point $\mathrm{O}$. If $\angle \mathrm{A}=56^{\circ}$, then $\angle \mathrm{BOC}$ equals:

Question 6:

In $\triangle A B C, \angle C=60^{\circ}, \angle A=75^{\circ}, A D \perp B C$, where $D$ is a point on $B C, B E \perp A C$ at $E$, where $E$ is a point on $A C . A D$ and $B E$ intersect each other at $\mathrm{H}$. What is the measure of $\angle \mathrm{CHD}$ ?

Question 7:

In a circle with centre O, chords AB and CD are parallel chords on opposite side of O. If AB = 20 cm, CD = 48 cm and the distance between the chords is 34 cm, then the diameter (in cm) of the circle is :

Question 8:

A circle inscribed in $\triangle P Q R$ with touches its side $P Q, Q R$ and $R T$ at point $S, T$ and $U$ respectively. If $P Q=12 \mathrm{~cm}, Q R=8 \mathrm{~cm}$, and $R P=16 \mathrm{~cm}$ then find the length of $P S, Q T$ and $R U$.

Question 9:

Sides $A B$ and $C D$ of a cyclic quadrilateral $A B C D$ are produced to met at $E$, and sides $A D$ and $B C$ are produced to meet at $F$. If $\angle A D C=75^{\circ}$, and $\angle B E C=50^{\circ}$ then the difference between $\angle B A D$ and $\angle A F B$ is.

Question 10:

$ABC$ is a triangle. $A B=5 \mathrm{~cm}, A C=\sqrt{41} \mathrm{~cm}$ and $B C=8 \mathrm{~cm}_{}$, $A D$ is perpendicular to $B C$. What is Area of triangle $ABD$?