Question

Let PQ and RS be tangents at the extremities 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 

Solution

Correct option is

The tangent PQ and RS meet at X.

                                                            

The point X lies on the circumference and we know the any diameters subtends a rt. Angle at any point on the circumference  

  

SIMILAR QUESTIONS

Q1

If the lines 3x – 4y – 7 = 0 and 2x – 3y – 5 = 0 are two diameters of a circle of area 49π square units, then the equation of the circle is:

Q2

A variable circle passes through a fixed point A(pq) and touches the x-axis. The locus of the other end of the diameter through A is:

Q3

A circle touches the x-axis and also touches the circle with centre (0, 3) and radius 2. The locus of the centre of the circle is:

Q4

The triangle PQR is inscribed in the circle x2 + y2 = 25. If Q and R have co-ordinates (3, 4) and (–4, 3) respectively than QPR is equal  to

Q5

Let AB be a chord of the circle x2 + y2 = a2 subtending a right angle at the centre. Then the locus of the centroid of the triangle PAB as Pmoves on the circle is

Q6

The lines joining the origin to the points of intersection of the line 4x + 3y = 24 with the circle (x – 3)2 + (y – 4)2 = 25 are

Q7

If the circles x2 + y2 + 2ax + cy + a = 0 and x2 + y2 – 3ax + dy – 1= 0 intersect in two distinct points P and Q then the line

5x + by – a = 0 passes through P and Q for:  

Q8

The intercept on the line y = x by the circle x2 + y2 – 2x = 0 is AB. Equation of the circle on AB as diameter is:

Q9

A square is formed by following two pairs of straight lines y2 – 14y + 45 = 0 and x2 – 8x + 12 = 0. A circle is inscribed in it. The centre of the circle is 

Q10

A diameter of x2 + y2 – 2x – 6y + 6 = 0 is a chord to circle (2, 1), then radius of the circle is