Question

Given a chord AB in a circle as shown

If two more chords AD and BE are drawn perpendicular to AB 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

Join DB and EA
In $\Delta DAB$ and $\Delta EBA$
(i) $\angle DAB=\angle EBA={90}^{\circ }$
(ii) AB=AB (Common)
(iii) $\angle ADB=\angle BEA$ [Angles in the same segment]
$\therefore \Delta DAB\cong \Delta EBA$ (RHS)
$\therefore AD=EB\left(CPCT\right)$