In right triangle ABC, right angled at 'B', AB = 18 cm. BD is perpendicular to AC such that AC = 2BD. If ∠BAC = ∠BCA, then find the numerical value of (AC2 - BD2).
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Correct answer: D
Explanation
Given: Right triangle ABC, right angle at B
AB = 18 cm
∠BAC = ∠BCA
Since ∠A = ∠C, opposite sides will be equal:
BC = AB = 18 cm
Now,
AC² = AB² + BC²
AC² = 18² + 18²
AC² = 324 + 324 = 648
So, AC = 18√2
Also, BD is perpendicular to AC and AC = 2BD
So, BD = AC/2 = 18√2/2 = 9√2
Now, BD² = (9√2)² = 81 × 2 = 162
Therefore, AC² − BD² = 648 − 162 = 486