SSC CHSL MATHS QUIZ

Question 1:

O is the centre of a circle with diameter 16 cm . T is a point outside the circle and TA is a tangent to a circle. If OT = 17 cm, what is the length (in cm) of the tangent TA?

15

20

24

26

Question 2:

What is the height (in $\mathrm{cm}$ ) of an equilateral triangle whose each side is 16 $\mathrm{cm}$ ?

$8 \sqrt{3}$

$6 \sqrt{2}$

$8 \sqrt{2}$

$6 \sqrt{5}$

Question 3:

In $\triangle L M N$, the bisectors of $\angle L$ and $\angle N$ intersect at an angle of $116^{\circ}$. What is the measure (in degrees) of $\angle M$ ?

72

64

52

44

Question 4:

A cyclic quadrilateral $\mathrm{ABCD}$ is drawn in a circle with centre $\mathrm{O} . \mathrm{A}$ and $\mathrm{C}$ are joined to $\mathrm{O}$. If $\angle \mathrm{ABC}=4 \mathrm{p}$ and $\angle \mathrm{ADC}=5 \mathrm{p}$, what is the measure (in degrees) of the $\angle \mathrm{AOC}$ reflex?

$220^{\circ}$

$160^{\circ}$

$200^{\circ}$

$180^{\circ}$

Question 5:

In a circle with centre $\mathrm{O}, \mathrm{PA}$ and $\mathrm{PB}$ are tangents to the circle at point $\mathrm{A}$ and point $\mathrm{B}$, respectively. $\mathrm{C}$ is a point on the major arc $\mathrm{AB}$. If $\angle \mathrm{ACB}=50^{\circ}$, then find the measure of $\angle \mathrm{APB}$.

$50^{\circ}$

$80^{\circ}$

$60^{\circ}$

$65^{\circ}$

Question 6:

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 $R U$.

$P S = 10{\mathrm{cm}}, Q T = 2{\mathrm{cm}}$ and RU = $8{\mathrm{cm}}$

$P S=12{\mathrm{cm}}, Q T=8{\mathrm{cm}}$ and RU= $10{\mathrm{cm}}$

$P S=10{\mathrm{cm}}, Q T=2{\mathrm{cm}}$ and RU =$6{\mathrm{cm}}$

$P S=6{\mathrm{cm}}, Q T=9{\mathrm{cm}}$ and RU =$10{\mathrm{cm}}$

Question 7:

In $\triangle A B C, \angle B$ is $50^{\circ}$ more than $\angle A$ and $\angle C$ is eight times of $\angle A$. The biggest angle is:

$110^{\circ}$

$104^{\circ}$

$108^{\circ}$

$96^{\circ}$

Question 8:

In $\Delta \mathrm{PQR}, \mathrm{S}$ is a point on $\mathrm{QR}$ such that $5 \mathrm{QS}$ $=3 Q R$. If each side of the triangle is $15 \mathrm{~cm}$, then find the value of PS?

$4 \sqrt{21}$

$3 \sqrt{23}$

$3 \sqrt{19}$

$5 \sqrt{26}$

Question 9:

If the sides of a quadrilateral ABCD touch a circle and $\mathrm{AB}=8 \mathrm{~cm}, \mathrm{CD}=7 \mathrm{~cm}, \mathrm{BC}=9 \mathrm{~cm}$, then the length of $\mathrm{AD}$ in $\mathrm{cm}$ is:

4 cm

6 cm

8 cm

9 cm

Question 10:

Two circles of radii $9 \mathrm{~cm}$ and $4 \mathrm{~cm}$ respectively touch each other externally at the point A. PQ is the direct common tangent of those two circles of centres $\mathrm{O}_{1}$ and $\mathrm{O}_{2}$ respectively. Then length of $\mathrm{PQ}$ is equal to:

$9$

$12$

$15$

$8$