Question

In a ΔABC, let BC = 3. D is a point on BC such that BD = 2, Then the value of AB² + 2AC² – 3AD² is ______.

Options

• 6.00

• 7.00

• 8.00

• 9.00

Answer 1

In a ΔABC, let BC = 3. D is a point on BC such that BD = 2, Then the value of AB² + 2AC² – 3AD² is 6.00.

Explanation:

Let F is foot of the perpendicular from A to BC.

∴ AB² = AF² + BF²

AC² = CF² + AF²

= (BC – BF)² + AF²

AD² = DF² + AF²

= (BD – BF)² + AF²

AB² + 2AC² – 3AD²

= AF² + BF² + 2(3 – BF)² + 2AF² – 3(2 – BF)² – 3AF²

= 6