Page 67 - Mathematics Class - X

OBSERVATIONS
We will observe that
1. ∆OAP and ∆OAQ completely cover each other. 2. Length of tangent AP = Length of tangent AQ

INFERENCE
This experiment verifies that tangents drawn from an external point to a circle are equal using paper folding.

EXTENDED TASK
1. Draw a circle of radius 5 cm and take a point 7 cm away from the centre. Construct two tangents and verify
that they are equal by actual measurement.
2. Create a beautiful design/model by using tangents of a circle. Few examples are shown here.

APPLICATION

Various other results of geometry can be proved using this result.

Viva-Voce

1. What is a tangent?
Ans. A tangent is a line that touches the circle at any point on the circumference of the circle without crossing it.
2. How many tangents can be drawn from a point to a circle?

Ans. Two tangents can be drawn from any point to a circle.
3. What do we name the common point of a tangent to a circle and the circle as?
Ans. It’s called the point of contact.

4. The word tangent comes from which Latin word?
Ans. TANGENT comes from the Latin TANGENS, the present participle of TANGERE which means “to touch’’.
5. What is the difference between the secant and tangent?
Ans. A tangent is a line that touches the circle at any point on the circumference of the circle whereas a
secant is a line that intersects the circle at two distinct points on the circumference of the circle.
6. Can the two tangents drawn at the end points of a diameter intersect at a point?
Ans. No, these tangents are parallel lines.

7. The radius of circle is 8 cm. What is the length of its longest chord?
Ans. 16 cm. Because the longest chord will be the diameter.

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