Chord of Contact

Q.

Which of the following is a point on the common chord of the circle $x^2+y^2+2x-3y+6=0$ and $x^2+y^2+x-8y-13=0$?

1. $(1,-2)$

2. $(1,4)$

3. $(1,2)$

4. $(1,-4)$

Q. If the chord of contact of tangents drawn from a point on the circle $x^2+y^2=a^2$ to the circle $x^2+y^2=b^2$ touches the circle $x^2+y^2=c^2$, then a, b, c are in .

1. H.P.
2. A.G.P.
3. A.P.
4. G.P.

Q.

Show that the tangents at the end points of a diameter of a circle are parallel.

Q.

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Q. If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD.

Q. Tap anything which represents the radius, length of tangent and the distance between the centre and the point

1. 5, 4, 3
2. 6, 8, 9
3. 25, 24, 7
4. 17, 15, 8
5. 10, 8, 6
6. 10, 13, 16
7. 8, 12, 15
8. 13, 12, 5

Q. Tap anything which represents the radius, length of tangent and the distance between the centre and the point

1. 5, 4, 3
2. 6, 8, 9
3. 25, 24, 7
4. 17, 15, 8
5. 10, 8, 6
6. 10, 13, 16
7. 8, 12, 15
8. 13, 12, 5

Q. Assertion :Statement-1: The line $x+9y-12=0$ is a chord of contact of a point $P$ with respect to the circle $2x^2+2y^2-3x+5y-7=0$. Reason: Statement-2: The line joining the points of contacts of the tangents drawn from a point $P$ outside a circle to the circle is the chord of contact of $P$ with respect to the circle.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is incorrect but Reason is correct
4. Both Assertion and Reason are incorrect

Q. If $A(1,p^2);B(0,1)$ and $C(p,0)$ are the co ordinates of three points then the value of p for which the area of triangle ABC is minimum, is

1. $\frac{1}{\sqrt{3}}$
2. $-\frac{1}{\sqrt{3}}$
3. $\frac{1}{\sqrt{3}}$ or $-\frac{1}{\sqrt{3}}$
4. None

Q. Prove that the area of the triangle formed by the tangents from the point $(x_1,y_1)$ and the chord of contact is $(y_1^2-4a{x}_1{)}^{\frac{3}{2}}÷2a$

Q.

In Fig., if AB = AC, prove that BE = EC [2 MARKS]

Q.

Show that the tangents at the end points of a diameter of a circle are parallel.