Question

IV.ANSWER THE FOLLOWING QUESTIONS:
21. The length of tangent from a point A at a distance of 5 cm from the centre of
the circle is 4 cm. What is the radius of the circle?
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Answer 1

Answer

Radius of the circle = 3 cm.

$\rule{200}1$

Solution

Given, a point A which is 5 cm from the centre of the circle. A tangent is drawn to the circle from point A. The length of tangent is 4 cm.

Let the centre of the circle be O. Let the point of contact of the tangent be 'B'. (Refer the attachment)

Now, we know that the radius is perpendicular to the tangent from the point of contact. Hence, OB is perpendicular to AB.

Now, let the radius of circle be 'r'. Hence, applying Pythagoras theorem, we get

r² + AB² = AC²

→ r² = AC² - AB²

→ r² = 5² - 4²

→ r² = 25 - 16

→ r² = 9

→ r = ±3 cm.

Since, length can not be negative, the radius of the circle would be 3 cm.

Answer 2

Answer:

radius 3 cm

Step-by-step explanation:

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