Challenges on Properties of Equal Chords and Distances of Chords from the Center
The chords AC...
Question
The chords AC and ZX are of same length. P is the center of the circle of radius 10 units. If ZY = 6 units, the length of PB is units.
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Solution
The distance of the chord ZX is represented by the perpendicular from the chord to the center, i.e., PY.
Hence, PZY forms a right triangle of hypotenuse PZ as radius of the circle. ∴PZ2=ZY2+PY2 ⇒PY=√PZ2−ZY2=√102+62 ⇒PY==√64=8 units
The chords AC and ZX are of same length.
Hence, they are equidistance from the center. ∴PY=PB=8 units