Tangent Secant Theorem

Q. Question 4
Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Q.

In the figure, PC is the tangent to the circle. A and B are 2 points on the circle. If $\angle$BPC $={60}^0$ and $\angle$APB $={55}^0$, then find $\angle$ABP .

1. 55°

2. 65°

3. 70°

4. 60°

Q.

Find the value of x

1. 46

2. 54

3. 56

4. 40

Q. MN is a tangent to the circle at the point of contact C. Identify the angle that is equal to x.

1. 
2. 
3. 

Q.

For a pair of linear equations, $a_1$=12, $b_1$= 2, $c_1$= 6 and $a_2$=24, $b_2$=4, $c_2$=7. Then the linear equation has

1. Two solutions

2. No solution

3. Four solutions

4. Infinite solutions

Q.

AB is diameter and AC is a chord of a circle such that $\angle BAC={30}^{\circ }$. If the tangent at C intersects AB produced in D, prove that BC = BD [4 MARKS]

Q. In the figure; PA is a tangent to the circle. PBC is secant and AD bisects angle BAC. Find the value of ∠CAD in terms of ∠PAB and ∠PBA.

Q.

Point (b, a) lies on the straight line ax + by –ab = 0. State with true or false.

1. True

2. False

Q. Question 8
A chord PQ of a circle is parallel to the tangent drawn at a point R of the circle. Prove that R bisects the arc PRQ.

Q.

In the figure, PC is the tangent to the circle. A and B are 2 points on the circle. If $\angle$BPC = ${60}^0$ and $\angle$APB = ${55}^0$, then find $\angle$ABP .

1. 55°

2. 60°

3. 65°

4. 70°

Q.

Find the value of $x$

1. 46

2. 54

3. 40

4. 56

Q. Which of the following equation has infinitely many solutions?

1. $6x+3=y+6x$
2. $2x+5=3$
3. $y-4=4-y$
4. $2x+5y=x-5y$

Q.

If $A=\left[\begin{array}{cc}2& 1\\ -1& 3\end{array}\right],B=\left[\begin{array}{cc}-3& 2\\ 4& 1\end{array}\right],C=\left[\begin{array}{cc}-3& 2\\ 4& 1\end{array}\right]$, verify the following :

(i) $A+B=B+A$

Q. Question 9
Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc.

Q. In the given figure PA = 7 cm and PB = 28 cm, the value of PT is equal to _______.
[2 Marks]

Q.

Let $A=\left[\begin{array}{ccc}1& -1& 2\\ 2& 1& 0\end{array}\right],B=\left[\begin{array}{ccc}0& 1& -1\\ 1& 2& 3\end{array}\right],\text{and}C=\left[\begin{array}{ccc}-1& 2& 3\\ 0& 0& 1\end{array}\right]$

Find each of the following :

(i) $A+B$

Q. The number of tangents that can be drawn at a point on the circle is

1. 0
2. 1
3. 2
4. Infinite