Circum Radius

Q.

Differentiate $\frac{sinx}{x}$ using the first principle.

Q. Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle, then 2r equals

1. 
2. 
3. 
4. 

Q. In $△ABC,$ sides opposite to angles $A,B,C$ are denoted by $a,b,c$ respectively. Then the value of $a\cos A+b\cos B+c\cos C=$

1. $2abc\sin A\cdot \sin B\cdot \sin C$
2. $2a\sin B\cdot \sin C$
3. $2c\sin A\cdot \sin B$
4. $2b\sin C\cdot \sin A$

Q. In a triangle $\Delta ABC$, the sum of the lengths of two sides is represented by $p$ and the product of the lengths of the same two sides is $q$. Let $c$ be the third side. If $p^2=c^2+2q$, then the area of the circumcircle of $\Delta ABC$ is

1. $\frac{\pi c^2}{2}$
2. $\pi c^2$
3. $2\pi c^2$
4. $\frac{\pi c^2}{4}$

Q. Which of the following relations hold true ?

1. $r=\frac{\Delta }{s},r=2Rsin\frac{A}{2}sin\frac{B}{2}sin\frac{C}{2}$
2. $r=\frac{\Delta }{s},r=Rsin\frac{A}{2}sin\frac{B}{2}sin\frac{C}{2}$
3. $r=\frac{\Delta }{s},r=2Rsin\frac{A}{3}sin\frac{B}{3}sin\frac{C}{3}$
4. $r=\frac{\Delta }{s},r=2Rsin\frac{A}{3}sin\frac{B}{2}sin\frac{C}{2}$

Q. Three circles with radii $a,b,c$ touch one another externally. If the tangents at contact points meet at point $I,$ then the distance of $I$ to the contact point of any two circles is:

1. $\sqrt{\frac{a+b+c}{abc}}$
2. $\frac{abc}{a+b+c}$
3. $\sqrt{\frac{abc}{a+b+c}}$
4. $\frac{a+b+c}{abc}$

Q. In a triangle $\Delta ABC$, the sum of the lengths of two sides is represented by $p$ and the product of the lengths of the same two sides is $q$. Let $c$ be the third side. If $p^2=c^2+2q$, then the area of the circumcircle of $\Delta ABC$ is

1. $\frac{\pi c^2}{2}$
2. $2\pi c^2$
3. $\frac{\pi c^2}{4}$
4. $\pi c^2$