Geometry Proof (need help)

The proof is explained below.

Step-by-step explanation:

Given a circle with centre O diameter AB and chord AD is drawn. another circle is drawn with AO as diameter to cut AD at C. we have to prove that BD=2OC.

In triangle ADB,

O is the mid point of side AB because O is the centre of diameter AB (given) and also

∠ACO = ∠ADB = 90° (angle subtended in semicircle)

Hence, OC║BD

Therefore, by converse mid point theorem C is also the mid-point of side AD.

Now, we get C and O is the mid-point of sides AD or AB

By midpoint theorem, the line joining the midpoints of the two sides of triangle is parallel to third side and is equal to half of the third

∴ OC=1/2BD

⇒ BD =2OC