Mathematics

Problem

\triangle ABC

is a right triangle with right angle at

B

. A perpendicular

BD

is drawn from

B

to the hypotenuse

AC

. a. (a) Prove that

\triangle ADB

is similar to

\triangle ABC

. b. (b) Prove that

\triangle BDC

is similar to

\triangle ABC

. c. (c) Using the results of parts (a) and (b), establish the relation

AC^{2} = AB^{2} + BC^{2}

. d. (d) If

AB = 6\,\text{cm}

and

BC = 8\,\text{cm}

, calculate the length of

AC

using the relation obtained in part (c).