Question

Segment AC is a diameter of circle P, which has a radius 13 cm. If B is a point on circle P such that AB = 10 cm, what is the length of segment BC?

Answer 1

Length of segment BC = 24 cm

Explanation:

It is given that AC is a diameter and B is a point on the circle P.

So, Δ ABC is a triangle in a semicircle and hence ∠ B = 90° as angle in a semicircle is a right angle.

It is also given that the length of the radius is 13 cm.

Therefore, diameter AC = 2 × radius = 2(13) = 26 cm.

It is given that AB = 10 cm.

From the right triangle Δ ABC,

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

`26^(2) =10^(2) +BC^(2)`

`BC^(2)=26^(2) -10^(2)`

`BC^(2)=576`

BC = 24 cm