Tangent

Q. $2\pi r$ is the formula for the of a circle.

1. area
2. perimeter
3. circumference

Q.

From the point $P(16,7)$, tangents $PQ$ and $PR$ are drawn to circle $x^2+y^2-2x-4y-20=0$.

If $C$ is the centre of the circle, then the area of equilateral $PQCR$ is

1. $450$ sq units

2. $15$ sq units

3. $50$ sq units

4. $75$ sq units

Q. In the given figure, which of the following options is incorrect?

दिए गए चित्र में, निम्नलिखित में से कौनसा विकल्प गलत है?

1. ΔABC ≅ ΔZXY
2. ΔXYZ ≅ ΔBCA
3. ΔACB ≅ ΔYZX
4. ΔCAB ≅ ΔYZX

Q. The equation of circle which touches the axes of coordinates and the line $fracx3+\frac{y}{4}$ and whose centre lies in the first quadrant is $x^2+y^2-2cx-2cy+c^2=0,$ where c is

1. 2
2. 3
3. 6
4. 1

Q. The two tangents to a circle from an external point are always

1. Equal

2. Perpendicular to each other

3. Parallel to each other
4. None of these

Q. The equation to the circle with centre (2, 1) and touching the line 3x + 4y = 5 is

1. $x^2+y^2-4x-2y+5=0$
2. $x^2+y^2-4x-2y-4=0$
3. $x^2+y^2-4x-2y-5=0$
4. $x^2+y^2-4x-2y+4=0$

Q. ABC is an isosceles triangle inscribed in circle. If AB = AC = $12\sqrt{5}$ cm and BC = 24 cm, find the radius of the circle.

Q.

The circle $C_1:x^2+y^2=3$ having centre at origin, O intersects the parabola $x^2=2y$ at the point P in the first quadrant. Let the tangent to the circle $C_1$ at P touches other two circles $C_2$ and $C_3$ at $R_2$ and $R_3$, respectively. Suppose $C_2$ and $C_3$ have equal radii $2\sqrt{3}$ and centres $Q_2$ and $Q_3$, respectively. If $Q_2$ and $Q_3$ lie on the Y-axis then

1. $Q_2{Q}_3=12$

2. $R_2{R}_3=4\sqrt{6}$

3. area of the $\Delta O{R}_2{R}_{3}is6\sqrt{2}$

4. area of the $\Delta P{Q}_2{Q}_{3}is4\sqrt{2}$