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:

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 27 Jul 2023 Shift 2)

Answer 1

Given:

BC = 16 cm, BD = 11 cm and ∠ADC = ∠BAC

Concept:

If two angles and a side of the two triangles are equal, then both triangles will be similar by AA property.

Calculation:

In ΔABC and ΔDAC

⇒ ∠ADC = ∠BAC

⇒ ∠C = Common angle in both triangle

So, ΔABC and ΔDAC are similar triangle.

⇒ $\frac{B C}{A C} = \frac{A C}{D C}$

⇒ AC² = BC × DC

⇒ AC² = 16 × 5 = 80

⇒ AC = 4√5

∴ The required result will be 4√5.

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