A chord AB is drawn in a circle centered at O. OC is the radius of the circle perpendicular to AB.
| April 9, 2021 | education
A chord AB is drawn in a circle centered at O. OC is the radius of the circle perpendicular to AB. Prove that the chords AC and BC are equal.
Since, by condition, the radius of the OС is perpendicular to the chord AB, the radius divides the chord in half. HB = HA = AB / 2.
Triangles ACH and BCH are rectangular, in which the leg CH is common, and leg HB = HA, then the triangles ACH and BCH are equal in two legs, then the chord AC is equal to BC, which was required to prove.
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