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If the sides of a cyclic quadrilateral are 3,3,4,4, show that a circle be inscribed in it. |
Answer» <html><body><p></p>Solution :Since, length of tangents from <a href="https://interviewquestions.tuteehub.com/tag/external-981194" style="font-weight:bold;" target="_blank" title="Click to know more about EXTERNAL">EXTERNAL</a> point to a circle are equal. <br/> `<a href="https://interviewquestions.tuteehub.com/tag/therefore-706901" style="font-weight:bold;" target="_blank" title="Click to know more about THEREFORE">THEREFORE</a>` AP=AS………(i) <br/> BP= BQ ……(ii) <br/> CR = CQ ………….(iii) <br/> <a href="https://interviewquestions.tuteehub.com/tag/dr-959219" style="font-weight:bold;" target="_blank" title="Click to know more about DR">DR</a>=DS…………..(iv) <br/> `therefore AB+ CD = (AP + <a href="https://interviewquestions.tuteehub.com/tag/pb-597752" style="font-weight:bold;" target="_blank" title="Click to know more about PB">PB</a>) (CR + DR)` <br/> `=(AS + BQ) + (CR + DS) <br/> =(AS+DS) + (BQ+CR)` <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/AAK_T3_MAT_C08_SLV_093_S01.png" width="80%"/> <br/> `rArr AB + CD = AD + BC`.....(1) <br/> `therefore` A circle can be inscribed in a <a href="https://interviewquestions.tuteehub.com/tag/quadrilatera-2965178" style="font-weight:bold;" target="_blank" title="Click to know more about QUADRILATERA">QUADRILATERA</a>, if sides of a quadrilateral satisfies (1) <br/> Sides of quadrilateral are 3,3,4,4. <br/> If we take AB=3, CD=4, BC=3, AD=4 <br/> `therefore AB+CD = BC + AD=7` <br/> `therefore` Circle is inscribed in quadrilateral ABCD. <br/> If sum of opposite sides of a quadrilateral is equal. only then a cirlcle can be inscribed in a quadrilateral.</body></html> | |