The tangents AB and AC are drawn from the point to the circle with the center O.

| September 12, 2021 | education

The tangents AB and AC are drawn from the point to the circle with the center O. Find the distance between points O and A, IF AC = 14cm and angle A = 120

Let’s construct the radii OS and OB to the points of tangency C and B.

The radii drawn to the points of tangency are perpendicular to the tangents themselves, then the triangles AOB and AOC are rectangular.

In right-angled triangles AOB and AOC, the hypotenuse OA is common, OB = OC = R, then the triangles AOB and AOC are equal in leg and hypotenuse, then the angle OAB = OAC = BAC / 2 = 120/2 = 60.

In a right-angled triangle AOC, the angle AOC = 90 – 60 = 30.

The AC leg lies opposite an angle of 30, then its length is equal to half the length of the OA hypotenuse.

OA = 2 * AC = 2 * 14 = 28 cm.

Answer: Between points O and A 28 cm.



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