Question

*The length of a tangent drawn from a point at a distance of 15 cm of circle is 12 cm. The radius of the circle is …………*

1️⃣ 8 cm
2️⃣ 9 cm
3️⃣ 10 cm
4️⃣ 11 cm​

Answer 1

Given : The length of a tangent drawn from a point at a distance of 15 cm of circle is 12 cm

To Find:   The radius of the circle  

1️⃣ 8 cm

2️⃣ 9 cm

3️⃣ 10 cm

4️⃣ 11 cm​

Solution:

Applying Pythagoras   theorem :

15²   = 12²  + (radius)²

=> 225 = 144 + (radius)²

=> 81 =(radius)²

=> 9² =(radius)²

=> 9 = radius

Radius of circle is  9 cm

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Answer 2

Given :- The length of a tangent drawn from a point at a distance of 15 cm of circle is 12 cm. The radius of the circle is …………*

1️⃣ 8 cm

2️⃣ 9 cm

3️⃣ 10 cm

4️⃣ 11 cm

Answer :-

we know that,

• The radius from the center of the circle to the point of tangency is perpendicular to the tangent line .

so, by pythagoras theorem we get,

→ (Radius)² + (Length of tangent)² = (Distance between tangent point and centre)²

putting given values,

→ r² + 12² = 15²

→ r² = 15² - 12²

→ r² = (15 + 12)(15 - 12)

→ r² = 27 * 3

→ r² = 81

→ r² = 9²

→ r = 9 cm (Option 2) (Ans.)

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