Answer:
Hence it is proved that AD.CB=AC.CD
Step-by-step explanation:
Given:
A circle with diameter AB and CD perpendicular to AB.
To Prove:
AD.CB=AC.CD
Solution:
Construct a circle with diameter AB and CD perpendicular AB
To get perpendicular Diameter AB ,point C must be on Y-axis with passing through center getting CD as radius of circle.
(Refer the Attachment)
Now,
we get two triangles, as ADC and CDB
So
Side(AD)=side(BD)
CD is common side
and Angle(ADC)=angle(BDC)
Using S-A-S test to triangles are similar
So their corresponding sides are in proportion ,
AD/BD=AC/BC
therefore
AD*BC=AC*BD
as BD=CD ........................... ( both are radius of the circle).
AD*BC=AC*CD
Hence it is required Proof.
