AB and CD are mutually perpendicular diameters of a circle. Chord CB is extended beyond point B by segment
| May 11, 2021 | education
AB and CD are mutually perpendicular diameters of a circle. Chord CB is extended beyond point B by segment BE equal to CB. What is the relative position of the line DE and the circle?
Consider the triangle CDE.
Point B, by condition, is the middle of the segment CE, BC = BE.
Point O is the center of the circle and divides the diameter CD in half, CO = DO.
Then the segment OB is the middle line of the triangle CDE, then OB is parallel to DE.
Diameters AB and CD are perpendicular by condition, then DE is perpendicular to CD.
Since the radius DО is perpendicular to the segment DE, the point D is the point of tangency, and the segment DE is tangent to the circle.
Answer: The segment DE is tangent to the circle.
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