Diameter AB of the circle is extended beyond point B to segment BC, CD-tangent to the circle, D-swing point.

| February 8, 2021 | education

Diameter AB of the circle is extended beyond point B to segment BC, CD-tangent to the circle, D-swing point. A chord parallel to CD is drawn through point B. The radius of the circle is 10 cm, and the distance from the center of the circle to the chord is 4 cm. Find AC.

Let’s extend the segment OK, the distance from the chord BM to the center of the circle, to the point of tangency D of the tangent and the circle. The segment OD is equal to the diameter of the circle and is perpendicular to the СD.

Consider the triangles СOD and ВOK, the CDO angle is straight, then the KВО angle is also straight, the same as, according to the condition of СD || ВM, the angles DСO and KВO are as equal as the corresponding angles at the intersection of parallel lines DС and ВC of the secant AC. Then the triangles СOD and ВOK are similar in two angles.

Then OD / OK = OС / OB.

OD = OB = R = 10 cm.

10/4 = OС / 10.

OС= 100/4 = 25 cm.

Then AC = OC + OA = 25 + 10 = 35 cm.

Answer: AC = 35 cm.



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