Question

Length of a tangent segment drawn from a point which is at a distance 12.5cm from the centre of a circle is 12cm, find the diameter of the circle​

Answer 1

Answer:

7 cm

Step-by-step explanation:

The tangent to a circle is perpendicular to a radius at the point of tangency.

If point O is the center of a circle, point A is the point of tangency and point B is at distance 12.5 cm from the center of the circle and 12 cm from the point of tangency.

Thus, ΔBAO is right angled and OA = r , AB = 12 cm , OB = 12.5 cm , m∠A = 90° .

r² + AB² = OB²

r² = 12.5² - 12² = 12.25 = 3.5² ⇒ f = 3.5 cm ⇒ d =2r = 7 cm

Answer 2

The diameter of the circle is 7 cm.

Given: OB$=12.5$ cm and AB$=12$ cm.

To find: Diameter of the circle.

Step-by-step explanation:

• Any straight line segment that passes through the center of the circle and whose endpoints are on the circle is called a circle's diameter. It can also be described as the circle's longest chord. Both definitions are correct for a sphere's diameter.

Solution:

• Let B be the external point, and OA be the circle's radius.

 By Pythagoras Theorem, in a right triangle, AOB;

⇒ $OB^{2} =AB^{2} +OA^{2}$

⇒ $AO^{2} =OB^{2}-OA^{2}$

∴ $12.52-122=12.25$

∴ $AO=3.5$ cm

Diameter: $2\times(AO)=2\times(3.5)$

⇒ $7$ cm