CDS GEOMETRY QUIZ 35

In $\triangle \mathrm{ABC}, \angle \mathrm{B}=68^{\circ}$ and $\angle \mathrm{C}=32^{\circ}$ sides $A B$ and $A C$ are produced to point $D$ and $E$, respectively. The bisector of $\angle \mathrm{DBC}$ and $\angle B C E$ meet at $F$. What is the measure of $\angle \mathrm{BFC}$ ?

$A B C$ is a triangle in which $A B=6 \mathrm{~cm}$, $B C=10 \mathrm{~cm}$ and $C A=8 \mathrm{~cm}$. What is the length of the altitude of the triangle drawn from vertex $A$ to $B C$?

$\triangle A B C$ is similar to $\triangle D E F$. The perimeters of $\triangle A B C$ and $\triangle D E F$ are $40 \mathrm{~cm}$ and $30 \mathrm{~cm}$ respectively. What is the ratio of $(B C+C A)$ to $(E F+F D)$ equal to?

$A B C D$ is a Cyclic quardrilateral. The side $A B$ is extended to $E$ in such a way that $B E=B C$, If $\angle A D C=70^{\circ}, \angle B A D=105^{\circ}$ then $\angle D C E$ is equal to?

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.

Find the circum - centre, of the triangle whose vertices are $(-2,5)(-3,0),(9,-6)$.

In the given figure, O is the center of the circle, and $\angle A O B=100^{\circ}$. Find $\angle A C B$? 

$\mathrm{PQ}$ and $\mathrm{PR}$ are tangents to a circle and $\mathrm{QR}$ is a chord, $\mathrm{PQ}=41 \mathrm{~cm}$ and $\mathrm{QR}=18 \mathrm{~cm}$, then find diameter of the circle.

If the two angles $(x-2)^{\circ}$ and $(2 x+5)^{\circ}$ are supplementary angles, then the complementary angles of $(x-3)^{\circ}$ is?

In a triangle $A B C$,  $D E$ is parallel to $B C, A D=6, B D=6$ $A E=a+3$, and $E C=8$. What is the value of ' $a$ '.