Question

The given figure shows a circle with radius O and diameter AB. The coordinates of points A and B are (2,3) and (4,5) respectively.

The length of the radius of the circle is:
a)
$1 \div 2 \sqrt{2}$
b)
$1 \div \sqrt{2}$
c)
$\sqrt{2}$
d)
$2 \sqrt{2}$








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Answer 1

Answer:

$diameter \: d = \sqrt{(x2 - x1) {}^{2} + (y2 - y1) {}^{2} } \\ = \sqrt{(4 - 2) {}^{2} + (5 - 3) {}^{2} } \\ = \sqrt{(2) {}^{2} +(2) {}^{2}} = \sqrt{4 + 4} \\ = \sqrt{16 } = 4$

hence, radius r= d/2

$r = \frac{4}{2} = 2$