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Question 1:

O is the centre of a circle with diameter 20 cm . T is a point outside the circle and TA is a tangent to a circle. If OT = 26 cm, what is the length (in cm) of the tangent TA?

Question 2:

ABCD is a cyclic quadrilateral whose diagonals intersect at E. If AB = BC, $\angle B A C=35^{\circ}$ and $\angle D B C=65^{\circ}$, then, $\angle DCE$ =?

Question 3:

The centroid of an equilateral triangle $\triangle \mathrm{ABC}$ is $\mathrm{G}$. If $\mathrm{AC}=30 \mathrm{~cm}$, and $\mathrm{AD}$ is a median then what is the length (in $\mathrm{cm}$ ) of AG is?

Question 4:

Tangents drawn from a point P outside a circle with center $\mathrm{O}$ are PA and PB. $A$ and $B$ are points on the circle. If $\angle A P B=120^{\circ}$ then $\frac{1}{2} \angle O A B$ is equal to :-

Question 5:

Two concentric circles having common centre 'O' and chord $\mathrm{AB}$ of the outer circle intersect the inner circle at points $\mathrm{C}$ and $\mathrm{D}$. If distance of chord from the centre is $3 \mathrm{~cm}$, outer radius is $13 \mathrm{~cm}$ and inner radius is 7 $\mathrm{cm}$, then length of $\mathrm{AC}$ in $\mathrm{cm}$ is:

Question 6:

In a Rhombus $\mathrm{ABCD}$, measure of angle $\mathrm{CAB}$ is $25^{\circ}$, What is the measure of angle $\mathrm{ABC} ?$

Question 7:

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 :

Question 8:

If each interior angle of a regular polygon is 11 times its exterior angle, the number of diagonals that can be drawn in the regular polygon is

Question 9:

$\triangle \mathrm{ABC}$ and $\triangle \mathrm{DEF}$ are similar and their areas be respectively $64 \mathrm{~cm}^{2}$ and $121 \mathrm{~cm}^{2}$. If $\mathrm{EF}=15.4$ $\mathrm{cm}, \mathrm{BC}$ is:

Question 10:

A circle inscribed in a triangle ABC touches its sides AB, BC and AC at the points D, E and F, respectively. If AB =29 cm, BC = 16 cm and AC = 19 cm, then the value of AD + BE + CF (in cm) is: