Circles Ex 10.1 Solutions
Question - 1 : - How many tangentscan a circle have?
Answer - 1 : -
There can be infinite tangents to a circle. A circle is made up ofinfinite points which are at an equal distance from a point. Since there areinfinite points on the circumference of a circle, infinite tangents can bedrawn from them.
Question - 2 : - Fill in the blanks:
(i) A tangent to a circleintersects it in …………… point(s).
Answer - 2 : -
(ii) A line intersecting a circle in two points is called a ………….
(iii) A circle can have …………… parallel tangents at the most.
(iv) The common point of a tangent to a circle and the circle is called …………
Answer:
(i) A tangent to a circle intersects itin one point(s).
(ii) A line intersecting a circle in twopoints is called a secant.
(iii) A circle can have two parallel tangents at themost.
(iv) The common point of a tangent to a circleand the circle is called the pointof contact.
Question - 3 : - A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at
Answer - 3 : -
a point Q so that OQ= 12 cm. Length PQ is :
(A) 12 cm (B) 13 cm
(C) 8.5 cm (D) √119 cm
Answer
In the above figure, the line that is drawnfrom the centre of the given circle to the tangent PQ is perpendicular to PQ.
And so, OP ⊥ PQ
Using Pythagoras theorem in triangle ΔOPQ weget,
OQ2 = OP2+PQ2
(12)2 = 52+PQ2
PQ2 = 144-25
PQ2 = 119
PQ = √119 cm
So, option D i.e. √119 cm is the length of PQ.
Question - 4 : - Draw a circle andtwo lines parallel to a given line such that one is a tangent and the
other, a secant tothe circle.
Answer - 4 : - 
In the above figure, XY and AB are two theparallel lines. The line segment AB is the tangent at point C while the linesegment XY is the secant.