Two perpendicular chords are drawn from a point on the circle, the difference of which is 4 cm.

| February 13, 2021 | education

Two perpendicular chords are drawn from a point on the circle, the difference of which is 4 cm. Find these chords if the radius of the circle is 10 cm.

Since the chords AB and AC are drawn from the same point and are perpendicular, the inscribed angle BAC = 90 and rests on the arc BC, the degree measure of which is 90 * 2 = 180.

Then the BC segment is the hypotenuse of a right-angled triangle and the diameter of the circle.

BC = 2 * R = 2 * 10 = 20 cm.

Let the length of the leg AB = X cm, then, by condition, AC = (X + 4) cm.

By the Pythagorean theorem, BC ^ 2 = AB ^ 2 + AC ^ 2.

400 = X ^ 2 + (X + 4) ^ 2.

X ^ 2 + X ^ 2 + 8 * X + 16 – 400 = 0.

2 * X ^ 2 + 8 * X – 384 = 0.

X ^ 2 + 4 * X – 192 = 0.

Let’s solve the quadratic equation.

X1 = -16. (Doesn’t fit because <0).

X2 = 12 cm.

AB = 12 cm.

AC = 12 + 4 = 16 cm.

Answer: The lengths of the chords are 12 cm and 16 cm.



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