Elementary Geometry

Geometry Level 2

In the above figure, $O$ is the center of circle. Angle $AOB = 90^\circ$ . The line $AC$ is parallel to $OD$ . $OB$ 's length is equal to twenty centimeters. $BD$ 's length is equal to four centimeters. Determine the length of $AB$ .

The answer is 24.

1 solution

Arpit MIshra
Apr 21, 2015

$OD$ the radius of the circle is equal to $OB + BD$ = $20 + 4 cm$ $= 24 cm$ .

$AC || OB$ and $AOBC$ is a rectangle. $OC = OD$ as $OC$ happens to be a radius of the circle like $OD$ . Therefore $OD$ = $24 cm$ .

Since Diagonals in a rectangle are equal so is $AB = OC$ therefore,

$AB = \boxed{24 cm}$

Elementary Geometry

The answer is 24.

1 solution

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