Radius of a circle with center 0 is 10cm Find the lenght of the chord if the chord is at a distance of 6cm From the centre.
Answers
Step-by-step explanation:
?
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.
Now, In right triangle OAC,
By Pythagoras Theorem
OA ² = AC² + CO²
Or, AC² = OA² - CO²
Or, AC² = 10² - 6² = 100 - 36 = 64
Or, AC² = 100 - 36
Or, AC² = 64
Or, AC² = 8²
Or, AC = 8
Or AB = AC + CB
Or AB = 8 + 8 ----------- (AC = CB)
Or AB = 16 cm
Therefore, length of chord = AB = 16 cm
Step-by-step explanation:
Let the circle be with center O and radius 10 cm. Let there be a chord AB
Draw a perpendicular from O on AB to meet at P. The perpendicular from the center divides the chord in two halves. Given, OP=6cm
Thus, In △OAP, Using Pythagoras theorem
OA
2
=AP
2
+OP
2
10
2
=AP
2
+6
2
AP
2
=64
AP=8 cm
Thus, AB=2AP=16 cm
Now, new chord CD is drawn with length 8 cm. Draw a perpendicular on CD from O to cut CD at N.
Now, In △ONC
OC
2
=NC
2
+ON
2
10
2
=4
2
+ON
2
ON=
84
cm