radius of a circle is 10 cm and distance of a chord from the centre is a 6 centimetre has the length of the chord. _____
Answers
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
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
ON=
84
cm