Question

In a circle with center O, a perpendicular is dropped from the center to a chord RT. Find the length of RO, if length of RT = 12 cm and QO = 8 cm.

Answer 1

The perpendicular from the centre of a circle to a chord bisects the chord.
$RT=12cm$
$\therefore RQ=QT=6cm$
Given, QO = 8 cm.
Using Pythagoras theorem in $\Delta RQO$,
we get, $(RO{)}^2=(QO{)}^2+(RQ{)}^2$
$\Rightarrow (RO{)}^2=8^2+6^2$
$\Rightarrow (RO{)}^2=100$
$\Rightarrow RO=10cm$.