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<img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_TRI_DPP_6_3_E01_294_S01.png" width="80%"> <br> Clearly points C, D, I and E are concyclic <br> `therefore angle EID = pi - C` <br> `therefore` In `Delta DEF, angle DFE =(pi-C)/(2)` <br> Similarly `angle EDF =(pi-A)/(2)` and `angle FED = (pi-B)/(2)` <br> `Delta' =2r^(2)sin((pi-A)/(2))sin((pi-B)/(2))sin((pi-C)/(2))` <br> `=2r^(2)cos((A)/(2))cos((B)/(2))cos((C )/(2))` <br> `therefore abc (a+b+c)(Delta')/(Delta^(3))` <br> `=(abc(a+b+c))/(Delta^(3))2r^(2)cos.(A)/(2)cos.(B)/(2)cos.(C )/(2)` <br> `=(abc(2s))/(Delta^(3))2r^(2)cos.(A)/(2)cos.(B)/(2)cos.(C )/(2)` <br> `=(abc(2s))/(Delta^(3))2r^(2)sqrt((s(s-a))/(bc))sqrt((s(s-b))/(ab))sqrt((s(s-c))/(ac))` <br> `=(4abcs)/(Delta^(3))r^(2)(s)/(abc)sqrt(s(s-a)(s-b)(s-c))` <br> `=(4s^(2))/(Delta^(2))r^(2)` <br> = 4.Transcript

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00:00 - 00:59 | hello everyone in this question we have liked the incircle of a triangle ABC touches the side BC and AD d e f respectively as I have already made the diagram you can see on your light area of triangle ABC with delta and that of triangle D E F G data if ABC side of triangle ABC then the value into a + b + c Delta dash by data cube is what we have four options so first of all we will repeat that as you can see if this than I can say that in radius a and b is equal to c i t point it man |

01:00 - 01:59 | girl ID is given by x minus angle angle angle angle angle d f by using the properties of circle I can say angle tiap he will be half of angle and that is why -35 similarly in that way we can also suggest for angle we also so we have angle angle ff5 -2 and similarly angle FD or you can say angle radius is 5 - know if I talk about area |

02:00 - 02:59 | of triangle d e f then by using the formula we have that angle as to angle TF and to let me clear it to ask sin angle of sin angle fdf2 FIR replace all the values here this area is given as talented as we have to ask whether this is fine but we have the value of DFT is 5 - to the value of a field is what 5 - 2 and the value of FD or you can say |

03:00 - 03:59 | now the value of delta dash is to ask this is sin 90 minus theta that is caused by 2 Cos pi by 2 Cos pi by 2 all the terms are in Multiplex that's right in a very proper Mela now what we need to find we need to find the abc into a + b + c into Delta dash by that are right now a b c are sides of triangle ABC perimeter of triangle ABC is given by a + b + c by 2 and the value of a + b + c is 25 substitute this value in my music equation then we have ABC this has to buy delta delta dash is what the value of delta Tashan to ask cost to cost |

04:00 - 04:59 | to cost right now I can write ABC square into S by Delta cube now I can write cause able to as as into x minus A similarly as into a minus b by AC and Research into x minus 3 by now we have 4 a b c are square as we have as as as as as as minus a minus b minus C square b square c square and its whole under I can write this for |

05:00 - 05:59 | ABC there is a b c are square as now if I take as a square and B have essay and one as remain inside minus a minus b minus C and under root of a square b square c square is what ABC and this is divided by right now what we have a b c will get cancel out this will become for area of triangle abc by heron's formula and that is Delta Square so Delta also get cancel out Delta you what delta delta delta is that cancel out and finally what we have we have four square nearby Delta Square and as we know that |

06:00 - 06:59 | Delta is equals to as this value get cancel out and my final answer is 4 so as per the given option option d is the correct option and this is my final thank you |