If a chord of length 6cm is at a distance of 4 cm from the centre, find the radius of the circle.
Answers
explanation:
-When we say “distance from the centre of the circle”, we mean the distance from the MIDPOINT of the chord to the centre of the circle. Any other point on the chord would be fine, but it would need to be specified in the problem.
-When we say “distance from the centre of the circle”, we mean the distance from the MIDPOINT of the chord to the centre of the circle. Any other point on the chord would be fine, but it would need to be specified in the problem.The solution is as follows:
-When we say “distance from the centre of the circle”, we mean the distance from the MIDPOINT of the chord to the centre of the circle. Any other point on the chord would be fine, but it would need to be specified in the problem.The solution is as follows:-Find the midpoint of the chord. 6/2=3. The midpoint of the chord is 3cm from each point on the chord that touches the circle, and 4 cm from the centre of the circle. Call the distance from the midpoint to the centre m, and half the chord length x. So m=4, and x=3.
-When we say “distance from the centre of the circle”, we mean the distance from the MIDPOINT of the chord to the centre of the circle. Any other point on the chord would be fine, but it would need to be specified in the problem.The solution is as follows:-Find the midpoint of the chord. 6/2=3. The midpoint of the chord is 3cm from each point on the chord that touches the circle, and 4 cm from the centre of the circle. Call the distance from the midpoint to the centre m, and half the chord length x. So m=4, and x=3.-We now have two sides of a right triangle with m and x. Inspection reveals that a line from the centre of the circle to the point where the chord touches the circle is the radius of the circle, and the hypotenuse of a right triangle. Call it r.
-When we say “distance from the centre of the circle”, we mean the distance from the MIDPOINT of the chord to the centre of the circle. Any other point on the chord would be fine, but it would need to be specified in the problem.The solution is as follows:-Find the midpoint of the chord. 6/2=3. The midpoint of the chord is 3cm from each point on the chord that touches the circle, and 4 cm from the centre of the circle. Call the distance from the midpoint to the centre m, and half the chord length x. So m=4, and x=3.-We now have two sides of a right triangle with m and x. Inspection reveals that a line from the centre of the circle to the point where the chord touches the circle is the radius of the circle, and the hypotenuse of a right triangle. Call it r.r^2=(m^2) + (x^2)= 9+16=25, so the radius is 5cm.
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