Inside a circle with a radius of 16 cm, point M is taken at a distance of 14 cm from the center, through which a chord 19 cm

| February 28, 2021 | education

Inside a circle with a radius of 16 cm, point M is taken at a distance of 14 cm from the center, through which a chord 19 cm long is drawn. Find the model of the difference in the lengths of the segments into which the point divides the chord.

Let us draw from point O, the center of the circle, a perpendicular to the chord CD and the radius of the OС.

In a right-angled triangle OCH, the length of the segment CH is equal to half the length of the chord CD.

AH = CD / 2 = 19/2 = 9.5 cm.

Then, by the Pythagorean theorem, OH ^ 2 = OC ^ 2 – CH ^ 2 = 256 – 90.25 = 165.75.

In the right-angled triangle OMН, according to the Pythagorean theorem, we determine the length of the segment MН.

MH ^ 2 = OM ^ 2 – OH ^ 2 = 196 – 165.75 = 30.25.

MH = 5.5 cm.

Then CM = CH – MH = 9.5 – 5.5 = 4 cm.

DМ = СD – СМ = 19 – 4 = 15 cm.

| DM – CM | = | 15 – 4 | = 11 cm.

Answer: The module of the difference between the segments is 11 cm.



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