Question

In the following figure, ∠ ACB = ∠ CDA. If AD = 6 cm and BD = 18 cm, find AC.

Answer 1

Given:
∠ ACB = ∠ CDA

Also, ∠ A = ∠ A (common angle)

So, triangles ΔACB and ΔCDA are similar by AA similarity, △ACB ∼ △CDA.

Thus,

`(AC)/(AD) = (AB)/(AC)`

Here given values, AD = 6 cm, BD = 18 cm,

AB = AD + BD

AB = 6 + 18

∴ AB = 24 cm

Now,

`(AC)/6 = 24/(AC)`

AC² = 144

∴ AC = 12 cm