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.

Answer 1

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.
$\therefore P{Z}^2=Z{Y}^2+P{Y}^2$
$\Rightarrow PY=\sqrt{P{Z}^2-Z{Y}^2}=\sqrt{{10}^2+6^2}$
$\Rightarrow PY==\sqrt{64}=8\text{units}$

The chords AC and ZX are of same length.
Hence, they are equidistance from the center.
$\therefore PY=PB=8\text{units}$