Question

A (p, 0), B(4, 0), C(5, 6), D(1, 4) are the vertices of a quadrilateral ABCD. If $\angle$ ADC is obtuse, the maximum integral value of p is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B

2

$cos\angle ADC=\frac{(AD{)}^2+(CD{)}^2-\left(AC{)}^2\right)}{2AD.CD}<0$
$\Rightarrow (P-1{)}^2+4^2+(5-1{)}^2+(64{)}^2<(P-5{)}^2+6^2$

$\Rightarrow 8P<24\Rightarrow P<3\to P=2$