Philippines
The length and breadth of a rectangle is ^@8 \space cm^@ and ^@15 \space cm^@. Find the radius of the circumcircle of this rectangle.
Answer:
^@8.5 \space cm^@
- The following figure shows the rectangle ^@ABCD^@ with its circumcircle,
^@AB^@ and ^@BC^@ are the length and the breadth of the rectangle ^@ABCD^@ and ^@AC^@ is the diameter of the circumcircle of the rectangle ^@ABCD^@.
According to the question, ^@AB = 15 \space cm,^@
^@ BC = 8 \space cm.^@ - ^@\begin{align} \text { Now, in the right-angled triangle } ABC, AC^2 & = AB^2 + BC^2 \\ \implies AC & = \sqrt { AB^2 + BC^2 } \\ & = \sqrt { (15)^2 + (8)^2 } \\ & = 17 \space cm \end{align}^@
- The diameter of the circumcircle of the rectangle ^@= 17 \space cm^@.
The radius of the circumcircle of the rectangle ^@= \dfrac { 17 }{2} = 8.5 \space cm^@.
