Question

A chord 6 cm long is drawn in a circle with a diameter equal to 10 cm. Then the perpendicular distance from the centre is​

Answer 1

O is the centre of circle, radius of the circle=OA=r=10 cm, AB = ?, OC = 6 cm, C is point on chord AB & OC perpendicular to AB.

$\text{Now, In right triangle OAC,}$

$\boxed{\bf{By\: Pythagoras\: Theorem}}$

$\sf OA ² = AC² + CO²$

$\sf Or, AC² = OA² - CO²$

$\sf Or, AC² = 10² - 6² = 100 - 36 = 64$

$\sf Or, AC² = 100 - 36$

$\sf Or, AC² = 64$

$\sf Or, AC² = 8²$

$\sf Or, AC = 8$

$\sf Or AB = AC + CB$

$\sf Or AB = 8 + 8 ----------- (AC = CB)$

Or AB = 16 cm

Therefore, length of chord = AB = 16 cm