Page 221 - ICSE Math 8

7. Two concentric circles C and C are of radii 5 cm and 3 cm respectively. Find the length of the chord
2
1
of circle C which is tangent to circle C at L.
2
1
8. In the given figure, LM and LN are tangents to a circle with centre O. Show that:
(a) LM = LP + PR
(b) LM + MN = Perimeter of ∆LPQ

9. In the adjoining figure, OB and OC are two tangents to the circle with centre
A and radius 3 cm. If OB = 4 cm, find the length of OA and the area of the
quadrilateral OBAC.
(Hint: Area of quadrilateral OBAC = 2 × Area of ∆ABO)

AT A GLANCE

¾ A circle is a set of points that are equidistant from a fixed point.
¾ A chord is a line segment joining any two points on a circle.
¾ A diameter is a chord passing through the centre of circle.
¾ The set of all the points which lie inside a circle is known as interior of the circle.
¾ The set of all the points which lie outside a circle is known as exterior of the circle.
¾ The set of all the points that lie inside and on the circle forms the circular region.
¾ An arc is a part of a circle between any two points on the circle.
¾ The region bounded by an arc and two radii of a circle is known as a sector.
¾ The region bounded by a chord and an arc of a circle is known as the segment of the circle.
¾ A tangent is a line that touches a circle at only one point. The point at which a tangent meets a circle is
known as its point of contact.
¾ A secant is a line that intersects a circle at two distinct points.
¾ One and only one tangent can be drawn through a point on the circle.
¾ From a point, two tangents can be drawn and both these tangents are of equal lengths.

MENTAL MATHS

1. Fill in the blanks.
(a) The centre of a circle lies in the ____________ of the circle.
(b) The longest chord of a circle is the ____________ of the circle.
(c) Through any point on the circumference of a circle, only ____________ tangent(s) can be drawn.
(d) A tangent to a circle touches the circle in ____________ point(s).
(e) The point of intersection of a tangent and the circle is called ____________.

2. Write True or False.
(a) The diameter of a circle is the length of its longest chord.

(b) The point where a secant meets a circle is known as its point of contact.
(c) The chord which passes through the centre of a circle is known as its diameter.
(d) At the point of contact, radius and tangent are perpendicular to each other.

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