ABC is a triangle and D is a point on the side BC. If BC = 16 cm, BD = 11 cm and ∠ADC = ∠BAC, then the length of AC is equal to:
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Correct answer: A
Explanation
The correct answer is option 1 i.e. cm.
In ΔABC and ΔDAC
⇒ ∠ADC = ∠BAC,
∠C = ∠C -------------(Common angle in both triangle)
the two triangles △BAC and △ADC are similar by the Angle-Angle (AA) similarity criterion.
By the properties of similar triangles, the corresponding sides are proportional.
Therefore,
⇒ BC/AC = AC/DC
BC = 16cm and BD = 11 cm, so:
DC = BC − BD = 16 cm − 11 cm = 5 cm
⇒ AC2 = BC × DC
⇒ AC2 = 16 × 5 = 80
⇒ AC = 4√5