### AC is the diameter of the semicircle and BD is perpendicular to AC. If AB = 8 cm and BC = 2 cm, find the length of BD.

4 cm

Step by Step Explanation:
1. The following figure shows the semicircle with the diameter AC,

According to the question, AB = 8 cm, and BC = 2 cm.
The diameter(AC) of the semicircle = AB + BC
= 8 + 2
= 10 cm
2. Let's draw a line OD from the center of the semicircle, as shown in the following figure,

The line OD, OA and OC are the radii of the semicircle.
Therefore, OD = OA = OC =
 AC 2

=
 10 2

= 5 cm
3. Now, OB = OC - BC
= 5 - 2
= 3 cm
4. In ΔOBD, ∠OBD = 90°
BD2 = OD2 - OB2 [By the Pythagorean theorem]
⇒ BD2 = 52 - 32
⇒ BD2 = 16
⇒ BD2 = 42
⇒ BD = 4 cm
5. Hence, the length of the BD is 4 cm.