2tangents are drawn from a point a which is 37 cm from the center of the circle. the diameter of the circle is 24 cm. what is the length of each tangent from point a to the point of the tangency?

35 cm

Step-by-step explanation:

Given : Diameter of a circle= 24 cm

Let r be the radius of the circle.

then

Since a tangent is always at right angles to the radius where it touches the circle.

Join the point A to the center of the circle such that it will become a right triangle with 37 cm as the longest sides [since it is the side opposite to the right angle.]

Let x denote the length of the tangents.

By Pythagoras theorem, we have

Hence, the length of each tangent from point a to the point of the tangency=35 cm

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: