Question

If a number of circles touch a given line segment PQ at a point A, then their centres lie on the perpendicular of PQ.

• A. True
• B. False

Answer 1

The correct option is A True

Given that PQ is any line segment and $S_1,S_2,S_3,S_4......$ circles are touch a line segment PQ at a point A . Let the centres of the circles $S_1,S_2,S_3,S_4.......$ be $C_1,C_2,C_3,C_4.....$ respectively.

Now, joining each centre of the circles to the point A on the line segment PQ by a line segment i.e $C_{1}A,C_{2}A,C_{3}A,C_{4}A\dots \dots .$ so on.
We know that, if we draw a line from the centre of a circle to its tangent line, then the line is always perpendicular to the tangent line.
Hence, the given statement is true.