ABC is a triangle and D is a point on the side BC If BC 12 cm BD 9 cm and ADC BAC then the length of...........

Quantitative Aptitude (CDS) Coordinate Geometry

ABC is a triangle and D is a point on the side BC. If BC = 12 cm, BD = 9 cm and $\small \angle$ ADC = $\small \angle$ BAC, then the length of AC is equal to

5 cm

6 cm

8 cm

9 cm

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Explanation:

In triangle ABC and triangle DAC
$\small \angle$ BAC = $\small \angle$ ADC
$\small \angle$ ACB = $\small \angle$ DCA (Common angle)
So , $\small \Delta$ ABC $\small \sim$ $\small \Delta$ DAC
Thus , BC / AC = AC / DC
=> 12 x 3 = AC x AC
=> AC² = 36
AC = 6 cm