Question

सिद्ध कीजिए कि किसी चक्रीय चतुर्भुज के अन्तः कोणों के अध्द्कों द्वारा बना हुआ चतुर्भुज भी चक्रिय होता है।

Answer 1

Step-by-step explanation:

bhai hindi ni aati itni lkl

Answer 2

The figure formed by joining the mid-points of the mid-points of the consecutive sides of a quadrilateral is Parallelogram

Given, ABCD is a parallelogram. Since, E and F are midpoints of the sides AB and CD respectively,

∴AE=BE=DF=CF

Here, for △HEB and △FHC,

∠EHB=∠FHC                [∵verticallyoppositeangles]

∠HFC=∠HBE                [Alternate interior angle so the lines AB∥CD and BF is transverse]

BE=CF

∴△HEB≅△FHC           [byAngle−Angle−Sideproperty]

In quadrilateral AECF,

AE=CF

and AE∥CF(asAB∥CD)

∴AECF is a parallelogram

[in a quadrilateral ,if apair of opposite sidesis equal and parallel then it is a parallelogram]

So, EC∥AF

⇒EH∥GF           ----------(1)

In quadrilateral BEDF,

BE=DF

and BE∥DF (a sAB∥CD)

∴BEDF is parallelogram

So, BF∥ED

⇒HF∥GE         -----------(2)

From (1) and (2) we get,

GEHF is a parallelogram.

p.s*  sorry for your answer in English hope u can understand it.