Question

In a circle with centre P, chord AB is drawn of length 13 cm, seg $PQ\perp$ chord AB, then find $l\left(QB\right)$.

Answer 1

A circle of centre $P$ is drawn,

Chord $AB$ is drawn of length 13cm as shown in figure. Let $Q$ is the point on $AB$ in such a way that $PQ$ ⊥ $AB$.

we know, the chord is bisected by a line passing through centre and perpendicular upon it. here,

chord $AB$ is perpendicular upon $PQ$.

so, $AQ=QB=\frac{AB}{2}$

$\Rightarrow AQ=QB=\frac{13}{2}=6.5$ cm

hence, length of $QB=6.5$ cm