Question

Через концы А и B дуги окружности с центром О проведены касательные АС и ВС. Меньшая дуга АВ равна 64 градуса. найдите угол АСВ.

Answer 1

через концы А и B дуги окружности с центром О проведены касательные АС и ВС. Меньшая дуга АВ равна 64 градуса. найдите угол АСВ.

Answer 2

I can answer your question in detail. Through the ends A and B of the arc of the circle with center O, the tangents AC and BC are drawn. The smaller arc AB is equal to 64 degrees. Find the angle ACB.

To solve this problem, we need to use the following facts:

- The radii OA and OB, drawn to the points of tangency A and B, are perpendicular to the tangents AC and BC, respectively . - The angle between the tangent and the chord, drawn from the point of tangency, is equal to half the measure of the intercepted arc. - The sum of the angles of a quadrilateral is 360 degrees.

Using these facts, we can find the angle ACB as follows:

- Since OA and OB are perpendicular to AC and BC, respectively, the angles OAC and OBC are right angles, and their measures are 90 degrees each . - Since the angle CAB is equal to the angle between the tangent AC and the chord AB, its measure is equal to half the measure of the arc AB, which is 64 degrees. Therefore, the angle CAB is 32 degrees. - Since the angle ACB is the opposite angle of the angle AOB in the quadrilateral AOBC, its measure is equal to the difference between 360 degrees and the sum of the measures of the angles OAC, OBC, and AOB. Therefore, the angle ACB is 360 - (90 + 90 + 64) = 116 degrees.

The answer is: The angle ACB is 116 degrees.