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Question

In a ABC, perpendicular AD from A on BC meets BC at D. If BD=8 cm, DC=2 cm and AD=4 cm, then

A
ABC is isosceles
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B
ABC is equilateral
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C
AC=2AB
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D
ABC is right angled at A
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Solution

The correct option is D ABC is right angled at A
In ABD, Using Pythagoras Theorem,
AD2+BD2=AB2
42+82=AB2
AB=80
In ACD, Using Pythagoras Theorem,
AD2+CD2=AC2
42+22=AC2
AC=20
Now, AB2+AC2=80+20=100
and, BC2=100
Since, AB2+AC2=BC2
Thus, ABC is a right angled triangle at A

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