Question 7. If 2AB = BC and the points A and B are A(4,6) and B(\alpha,\beta) respectively, then \alpha + 2\beta is equal to
(1) 42
(2) 39
(3) 48
(4) 45
Answer (1)
Explanation:
Let the angle bisector from B meet AC at D.
Given, 2AB = BC
So, AB : BC = 1 : 2
By the angle bisector theorem, AD : DC = 1 : 2
Since B lies on the angle bisector y = x,
\alpha = \betaUsing the section ratio on line AC,
\frac{4-\alpha}{6-\alpha} = \frac{10}{8}Solving, \alpha = 14
Hence, \beta = 14
Therefore, \alpha + 2\beta = 14 + 28 = 42