Circles Ex- 10.1

Hi Friends and Champs!

Before proceeding with the next exercise, we need to understand some basic points of Circle.

Circle is a collection of points, which are at equidistant from a fixed point.
Tangent to a circle, is a straight line, which touch the circle at exactly only one point.
A point on the circle can have a maximum of only one tangent.
A straight line which intersects a circle at exactly two points called secant, which coincide the chord from the same intersected points.
The word tangent taken from the latin word tangere which means to touch.
Common point of a circle and a tangent is called point of contact.
A tangent is always perpendicular to the radius of the circle passes thru the point of contact and center of the circle.

In the above figure PQ is a tangent of a circle centre at "O" with radius R and point of contact of circle and tangent PQ is "C".

Exercise - 10.1

1. How many tangents can a circle have?

Solution:

A circle is a collection of infinitely many points, hence a circle may have infinitely many tangents.

2. Fill in the blanks :

(i) A tangent to a circle intersects it in point (s). Only one

(ii) A line intersecting a circle in two points is called a secant

(iii) A circle can have parallel tangents at the most. exactly two at opposite circle points.

(iv) The common point of a tangent to a circle and the circle is called .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.

Solution:

OQ = 12 cm (given)

PO = 5 cm (given)

since PQ is a tangent, therefore PQ ⊥ PO and so <P is a right angle , therefore

OQ²=PO²+PQ²

12²=5²+PQ²
144 = 25 +PQ²

PQ²= 119

PQ = √119 cm Ans.

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.

Solution:

I hope all the questions are properly readable and understandable, in case of some confusion, kindly let me know in comment section 🙏🙏🙏.

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