Question

In Fig. 3, angal ACB = 90° and CD perpendicular AB, prove that
CD square = BD X AD.
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Answer 1

here is your answer

dear MaTe

GIVEN

ABC= 90°

CD ic perpendicular to AB

To prove that CD² = BD × AD

In Δ CAD, CA² = CD² + AD².....(1)

In Δ CDB, CB² = CD² + BD² ... (2)

(1)+(2) equation

we get,

CA² + CB² = 2CD² + AD² + BD²

AB² = 2CD² + AD² + BD²

AB² - AD² = BD² + 2CD²

(AB + AD)(AB - AD) - BD² = 2CD²

(AB + AD)BD - BD² = 2CD²

BD(AB + AD - BD) = 2CD²

BD × 2AD = 2CD²

CD² = BD × AD

Hence proved.