From point A to the circle, 2 tangents AB and AC were drawn, the radius of the circle is 7 cm, AB = 24 cm.Find the chord BC

univerkov | August 28, 2021 | education

By the property of the tangent, the radius OB is perpendicular to the tangent AB, then the triangle AOB is rectangular, in which, according to the Pythagorean theorem, we determine the length of the hypotenuse OA.

OA ^ 2 = OB ^ 2 + AB ^ 2 = 49 + 576 = 625.

ОА = 25 cm.

Determine the area of the triangle AOB. Saov = ОВ * AB / 2 = 7 * 24/2 = 84 cm2.

Also Saov = OA * BH / 2.

BH = 2 * Saov / OA = 2 * 84/25 = 6.72 cm.

Rectangular triangles AOB and AOC are equal in leg and hypotenuse, then CH = BH = 6.72 cm. BC = 2 * BH = 2 * 6.72 = 13.44 cm.

Answer: The length of the BC chord is 13.44 cm.

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