Question

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

Answer 1

Answer:

7cm

Step-by-step explanation:

since tangent is normal to radius of circle..

(radius)^2= 12.5^2-12^2

radius = 3.5

diameter = 7cm

Answer 2

Given :

• Length of a tangent segment drawn from a point , which is at a distance of 12.5cm from the centre of a circle is 12cm.

To Find :

• Diameter of circle = ?

⠀⠀

Figure :

$\setlength{\unitlength}{20}\begin{picture}(6, 3) \put(2, 2){\circle{14}}\put(2, 2){\circle*{0.1}}\put(2, 2){\line(0, 1){1}}\put(2, 2){\line(1, 0){3}}\put(5, 2){\line( - 3, 1){3}}\put(2, 2.7){\line(1,0 ){0.2}}\put(2.2, 2.7){\line(0, 1){0.2}}\put(5, 2){ \bf P }\put(2,3.2 ){ \bf Q }\put(1.8,1.5 ){ \bf O }\put(3, 1.5){ \bf 12.5 \: cm }\put(3, 2.8){ \bf 12 \: cm }\end{picture}$

Solution :

Let the OQ be the radius of circle and external point be the P.

So,

PQ = 12 cm

OP = 12.5 cm

In right triangle, ∆QOP

$\dashrightarrow\:\sf OQ = \sqrt{AB{^2} - OB{^2}} \ \\ \\ \ \dashrightarrow\:\sf OQ = \sqrt{12.5{^2} - 12{^2}} \ \\ \\ \ \dashrightarrow\:\sf OQ = \sqrt{12.25} \\ \\ \pink\dashrightarrow\:\pink{ \sf OQ = 3.5 }$

So,

→ Diameter = 2 × Radius

→ Diameter = 2 × 3.5

→ Diameter = 7 cm

Therefore, the diameter of circle is 7 cm.