Two mutually perpendicular chords are drawn in the circle. The largest of them is 10 cm, it is 3 cm

| February 4, 2021 | education

Two mutually perpendicular chords are drawn in the circle. The largest of them is 10 cm, it is 3 cm away from the center of the circle, and the second chord is 4 cm away from the center of the circle, find the second chord

The segment OK is perpendicular to the chord AB, which means it divides it in half, then AK = ВK = AM / 2 = 10/2 = 5 cm.

Let’s finish the radius OA, then in a right-angled triangle AOK, according to the Pythagorean theorem, OA ^ 2 = AK ^ 2 + OK ^ 2 = 25 + 9 = 34.

The OH segment is perpendicular to the chord СD, then DН = CH = СD / 2.

Let’s draw the radius of OD.

OD ^ 2 = OA ^ 2 = 32.

In a right-angled triangle ODН, DН ^ 2 = OD ^ 2 – OH ^ 2 = 32 – 16 = 16.

DН = 4 cm.

Then СD = 2 * DН = 8 cm.

Answer: The length of the second chord is 8 cm.



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