ABC is a right angle triangle at A and AD is perpendicular to the hypotenuse then BD / CD is equals to
a. (AB/CD)^2
b. (AB/AD)^2
c. AB/AC
d. AB/AD
With detailed solution.
Answers
The value of BD/CD is (AB/AC)² [ correct option is not mentioned in question. ]
ABC is a right angle triangle at A and AD is perpendicular to the hypotenuse.
We have to find the BD/CD.
See figure attached in solution,
Here We draw a right angled triangle ABC which is right angle at A and AD is drawn perpendicular to the hypotenuse BC.
From ∆ABD and ∆ABC,
∠ADB = BAC = 90°
∠ABD = ∠ABC [ common angle ]
from A - A rule,
∆DBA ~ ∆ABC
∴ BD/AB = AB/BC = AD/AC
⇒BD × BC = AB² ....(1)
Similarly, from ∆ADC and ∆ABC,
∠ADC = ∠CAB = 90°
∠ACD = ∠ACB [ common angle ]
from A - A rule,
∆DCA ~ ∆ACB
∴ CD/AC = AC/BC = AD/AB
⇒CD × BC = AC² ....(2)
Dividing equation (1) by (2) we get,
⇒BD/CD = AB²/AC² = (AB/AC)²
Therefore the value of BD/CD is (AB/AC)².
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