Q19 of 100 Page 17

Prove that the perpendicular bisectors of the sides of a cyclic quadrilateral are concurrent.

Let ABCD be a cyclic quadrilateral and let O be the centre of the corresponding circle

Then, each side of the equilateral ABCD is a chord of the circle and the perpendicular bisector of a chord always passes through the centre of the circle


So, right bisectors of the sides of the quadrilateral ABCD will pass through the centre O of the corresponding circle.


More from this chapter

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17

In Fig. 16.188, ABCD is a cyclic quadrilateral. Find the value of x.

 18

ABCD is a cyclic quadrilateral in which:

(i) BC||AD, ∠ADC=110° and ∠BAC=50°. Find ∠DAC.


(ii) ∠DBC=80° and ∠BAC=40° Find ∠BCD.


(iii) ∠BCD=100° and ∠ABD=70°. Find ∠ADB.

 20

Prove that the centre of the circle circumscribing the cyclic rectangle ABCD is the point of intersection of its diagonals.

 21

Prove that the circles described on the four sides of a rhombus as diameters, pass through the point of intersection of its diagonals.