Question

A semi-circle is drawn outwardly on chord AB of the circle with centre O and radius sqrt(8)cm .The perpendicular from O to AB meets the semi-circle at C .Find the length of chord AB so that the line segment OC has the maximum length.​

Answer 1

Answer:

From C a point on AB a line perpendicular to AB is drawn meeting the circumference of the semicircle ... Let O be the centre of the circle. ... PQRS is a diameter of a circle whose radius is

Answer 2

Answer:

Length of chord AB is 4cm for maximum length of OC.

Step-by-step explanation:

Let the length of OC be D

D = $\sqrt{8-r^{2} } + r$

dD/dr = $-r/\sqrt{8-r^{2} } + 1$

for maximum of D , dD/dr = 0

0 =    $-r/\sqrt{8-r^{2} } + 1$

$8-r^2 = r^2$

$8 = 2r^2$

r = 2

AB = 2r = 4 cm

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