Question

In $\Delta ABC,AB=8,AC=6,$ Altitude AD = 4.8. AE is the diameter of the circumcircle. Find the circumradius.

• A. 5
• B. 10
• C. 15
• D. Cannot be determined

Answer 1

The correct option is A

5

In $\Delta ABDand\Delta AEC$
$m\angle ADB=m\angle ACE$ (both ${90}^{\circ })$
$m\angle ABC=m\angle AEC$
$\therefore \Delta ABD-\Delta AEC$ (AA similarity)
$\frac{AB}{AE}=\frac{AD}{AC}$ (Proportional sides)
$\therefore AE=\frac{AB}{AD}\times AC=\frac{8}{4.8}\times 6=10$
$\therefore$ Circumradius = 5