SOLUTION: Triangle ACB is in inscribed in cicle o. Given: AB is diameter and CD is perpendicular to AB. Prove: (CD)^2=(AD)(DB).

Algebra ->  Algebra  -> Geometry-proofs -> SOLUTION: Triangle ACB is in inscribed in cicle o. Given: AB is diameter and CD is perpendicular to AB. Prove: (CD)^2=(AD)(DB).      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 193358This question is from textbook Essentials of Geometry for College Students
: Triangle ACB is in inscribed in cicle o. Given: AB is diameter and CD is perpendicular to AB. Prove: (CD)^2=(AD)(DB).This question is from textbook Essentials of Geometry for College Students

Answer by jojo14344(1482) About Me  (Show Source):
You can put this solution on YOUR website!



Prove:

We know , and

We can see the triangle is split into 2 Isosceles Right Triangles.
Theorem:
In an isosceles right triangle, the sides are in the ratio
The equal sides make the right angle.

Therefore, equal sides ---> AD=DB=CD=Radius=(1/2)(AB)

Proving:
= -->
= -->
= --> ; *Note: AD=DB=CD=Radius=(1/2)(AB)

Thank you,
Jojo