Question

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

Solution

## 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, $$AQ = QB = \dfrac {AB} {2}$$$$\Rightarrow AQ = QB = \dfrac {13} 2 = 6.5$$ cm hence, length of $$QB = 6.5$$ cmMathematics

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