Login/Sign Up
Home » We have to prove that the line segment joining the midpoints of two parallel chords of a circle passes through its center.
We have to prove that the line segment joining the midpoints of two parallel chords of a circle passes through its center.
Circles | Class 10 | Frank | Guides | ICSE | Maths
We have to prove that the line segment joining the midpoints of two parallel chords of a circle passes through its center.

Let’s assume AB and CD is the two parallel chords of the circle having Q and P as their mid-points, respectively.

Let the Circle has the center O.

Construction: Join OP and OQ and draw EF||AB||CD. Since, CD has the mid-point.

OP\bot CD(It is perpendicular)

\angle CPO=\angle DPO={{90}^{\circ }}

But OF||CD

∴ \angle POF=\angle CPO… [alternate interior angle of the parallel lines]

\angle POF={{90}^{\circ }}

Similarly,\angle FOQ={{90}^{\circ }}

Now, \angle POF+\angle FOQ={{90}^{\circ }}+{{90}^{\circ }}={{180}^{\circ }}

Therefore, POQ is a straight line.

Hence proved that the line segment joining the midpoints of two parallel chords of a circle passes through its center.

i

More Material