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 .
Step-by-Step Solution
Key Concept: Recall the basic definitions related to a circle: • Tangent – a straight line that touches the circle at exactly one point. The point of touching is called the *point of contact* (or point of tangency). • Secant – a straight line that cuts the circle at two distinct points. • At most two tangents to a given circle can be parallel to each other (e.g., the top and bottom horizontal tangents).
1. Tangent and its point of contact
- By definition, a tangent touches the circle at exactly one point. That unique point is termed the *point of contact* (also called point of tangency). Hence, the blank (i) is filled with point of contact.
2. Line intersecting a circle at two points
- A straight line that meets the circle in two distinct points is called a *secant*. Therefore, blank (ii) is secant.
3. Maximum number of parallel tangents
- Through any circle, at most two tangents can be drawn that are parallel to each other (think of the horizontal tangents at the top and bottom of the circle). Hence, blank (iii) is two.
4. Common point of a tangent and the circle
- The single point where a tangent touches the circle is again the *point of contact*. Thus, blank (iv) is point of contact.
Putting all the answers together:
(i) point of contact
(ii) secant
(iii) two
(iv) point of contact
Correct Answer: (i) point of contact, (ii) secant, (iii) two, (iv) point of contact