Question

ABC is an isosceles triangle and a circle such that it passes through vertex C and AB acts as a tangent at D for the same circle. AC and BC intersects the circle at E and F respectively AC = BC = 4 cm and AB = 6 cm. Also, D is the mid-point of AB. What is the ratio of EC : (AE + AD)?

• A. 1 : 2
• B. 1 : 3
• C. 2 : 5
• D. None of these

Answer 1

The correct option is B 1 : 3

Here, AC and BC are the secants of the circle and AB is trangent at D
$\therefore AE\times AC=A{D}^{2}AE\times 4=(3{)}^2\Rightarrow AE=\frac{9}{4}\therefore CE=4-\frac{9}{4}=\frac{7}{4}\therefore CE:(AE+AD)=\frac{7}{4}:(\frac{9}{4}+3)=\frac{7}{4}:\frac{21}{4}=1:3$