Access Answers for SAT Maths Chapter 10 – Circles
Exercise: 10.1
1. How many tangents can a circle have?
Answer:
There can be infinite tangents to a circle. A circle is made up of infinite points which are at an equal
distance from a point. Since there are infinite points on the circumference of a circle, infinite
tangents can be drawn from them.
2. Fill in the blanks:
(i) A tangent to a circle intersects it in …………… point(s).
(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 it in one point(s).
(ii) A line intersecting a circle in two points is called a secant.
(iii) A circle can have two parallel tangents at the most.
(iv) The common point of a tangent to a circle and the circle is called the point of contact.
3. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at
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 drawn from the centre of the given circle to the tangent PQ is
perpendicular to PQ.
And so, OP ⊥ PQ
, Using Pythagoras theorem in triangle ΔOPQ we get,
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.
4. Draw a circle and two lines parallel to a given line such that one is a tangent and the
other, a secant to the circle.
Answer:
In the above figure, XY and AB are two the parallel lines. The line segment AB is the tangent at point
C while the line segment XY is the secant.
Exercise: 10.2
In Q.1 to 3, choose the correct option and give justification.
1. From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the
centre is 25 cm. The radius of the circle is
(A) 7 cm
(B) 12 cm
(C) 15 cm
(D) 24.5 cm
Answer:
Exercise: 10.1
1. How many tangents can a circle have?
Answer:
There can be infinite tangents to a circle. A circle is made up of infinite points which are at an equal
distance from a point. Since there are infinite points on the circumference of a circle, infinite
tangents can be drawn from them.
2. Fill in the blanks:
(i) A tangent to a circle intersects it in …………… point(s).
(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 it in one point(s).
(ii) A line intersecting a circle in two points is called a secant.
(iii) A circle can have two parallel tangents at the most.
(iv) The common point of a tangent to a circle and the circle is called the point of contact.
3. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at
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 drawn from the centre of the given circle to the tangent PQ is
perpendicular to PQ.
And so, OP ⊥ PQ
, Using Pythagoras theorem in triangle ΔOPQ we get,
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.
4. Draw a circle and two lines parallel to a given line such that one is a tangent and the
other, a secant to the circle.
Answer:
In the above figure, XY and AB are two the parallel lines. The line segment AB is the tangent at point
C while the line segment XY is the secant.
Exercise: 10.2
In Q.1 to 3, choose the correct option and give justification.
1. From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the
centre is 25 cm. The radius of the circle is
(A) 7 cm
(B) 12 cm
(C) 15 cm
(D) 24.5 cm
Answer:
