Q11 of 63 Page 145

Prove that the line segment joining the mid-points of two parallel chords of a circle passes through the centre of the circle.


Let AB and CD be the two parallel chords of a circle such that M and N are the mid-points of AB and CD respectively.


Since the perpendicular bisector of the chord passes through the centre,


⇒ ON ⊥ CD and OM ⊥ AB


Since AB || CD, NOM is a straight line.


Hence the line joining the midpoints of two parallel chords of a circle passes through the centre of the circle.


More from this chapter

All 63 →
9

The vertices of quadrilateral ABCD lie on a circle such that AB = CD. Then prove that AC = BD.

 10

If two equal chords of a circle intersect each other then prove that the ordered points of one chord are respectively equal to the corresponding points of the record chord.

 1

Write True/False for each and write the reason also for your answer.

(i) The angles subtended at any two points lying of the circle by every chord are equal.


(ii) In figure, AB is a diameter of a circle and C is any point on the circle. Then AC2 + BC2 = AB2.


(iii) In figure 12.48, if ∠ADE = 120°, then ∠EAB = 30°.


(iv) In figure 12.48, ∠CAD = ∠CED.


 2

In figure, ∠ABC = 45°. Then prove that OA ⊥ OC.