Question

AB¯¯¯¯¯is a radius. CD←→is tangent to circle A at point B, where AB=7 and EC=18. What is BC?

Circle with center point A. Radius AB is drawn. Tangent line CD is drawn and intersects the circle at point B. Segment AC is drawn from the center point A through point E on the circle to point C on line CD. The lengths of segments are not provided.

BC =

Answer 1

BC is 24 units

Explanation:

Given that: AB = 7 units

EC = 18 units

From a sketch for the question, we have a triangle ABC. Such that:

AC = AE + EC

But,

AE = AB = 7 (radius of the circle)

So that,

AC = 7 + 18

= 25 units

Applying Pythagoras theorem to triangle ABC, we have:

`/AC/^(2)` =
`/AB/^(2)` +
`/BC/^(2)`

`25^(2)` =
`7^(2)` +
`/BC/^(2)`

`/BC/^(2)` = 625 - 49

= 576

BC =
`√(576)`

= 24

Thus, BC is 24 units.