Ex.10.1 Q2. CIRCLES Solution - NCERT Maths Class 10

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Question

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 _________ .

Text Solution

 

Steps:

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

Reasoning:

A tangent to a circle is a line that intersects the circle at only one point.

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

Reasoning:

Secant is a line that intersects the circle in two points.

(iii) A circle can have    Two     parallel tangents at the most.

Reasoning:

Tangent at any point of a circle is perpendicular to the radius through the point of contact. Extended radius is a diameter which has two end points and hence two tangents which are parallel to themselves and perpendicular to the diameter.

Center \(O,\) diameter \(AB,\text{ tangents}\, PQ, RS\) and, \({PQ}\; \| \;{RS}\)

\(A\) and \(B\) are called as point of contact.

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

Reasoning:

A tangent to a circle is a line that intersects the circle at only one point and that point is called as point of contact.

 

  
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