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 🙏🙏🙏.