Question

If two chords AD and BE are drawn perpendicular to a chord AB of a circle which of the following is correct?

• A. AD=BE
• B. AD=2BE
• C. 2AD=BE
• D. AD=3BE

Answer 1

The correct option is A AD=BE

Now for $\Delta$ ABD and $\Delta$ BAE:
i.) Side AB is common
ii.) $\angle$ DAB = $\angle$ EBA (right-angle)
iii.) And side BD = side AE (both are equal to twice the radius of circle)
(Point C is the centre of circle as angle ABE is a right angle)

$\Rightarrow \Delta ABD\cong \Delta \text{BAE (by S-A-S congruency)}$

So, side AD = side BE (corresponding sides of congruent triangles)