Question : In $\triangle \mathrm{ABC}$, AB = AC, and D is a point on side AC such that BD = BC. If AB = 12.5 cm and BC = 5 cm, then what is the measure of DC?
Option 1: 2 cm
Option 2: 2.5 cm
Option 3: 3 cm
Option 4: 1.8 cm
Correct Answer: 2 cm
Solution :
$\triangle $ABC, AB = AC
and D is a point on side AC such that BD = BC.
Here, AB = 12.5 cm and BC = 5 cm
⇒ $\triangle$ABC ~ $\triangle$BDC
⇒ $\frac{DC}{BC}$ = $\frac{BC}{AC}$
⇒ $\frac{DC}{5}$ = $\frac{5}{12.5}$
⇒ DC = 2 cm
Hence. the correct answer is 2 cm.
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