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(a) area of the triangle XYZ is `6sqrt6`(b) the radius of circumcircle of the triangle XYZ is `(35)/(6) sqrt6`(c) `sin.(X)/(2) sin.(Y)/(2) sin.(Z)/(2) = (4)/(35)`(d) `sin^(2) ((X + Y)/(2)) = (3)/(5)`

Answer :

A::C::DSolution :

`(s-x)/(4) = (s-y)/(3) = (s-z)/(2) = (3s -(x +y + z))/(9) = (s)/(9)` <br> `:. x = (5s)/(9), y = (2s)/(3), z = (7s)/(9)` <br> Area of incircle `pi r^(2) = (8pi)/(3) rArr r^(2) = (8)/(3)` <br> `rArr Delta^(2) = r^(2) s^(2) = (8s^(2))/(3)` <br> `rArr s.(4s)/(9) .(s)/(3).(2s)/(9) = (8)/(3) s^(2)` <br> `rArr s = 9` <br> `:. Delta = sqrt((8)/(3)) xx 9 = 6 sqrt6` sq. units <br> `R = (xyz)/(4Delta) = ((5s)/(9).(2s)/(3).(7s)/(9))/(4 xx 6 sqrt6) = (35)/(24) sqrt6` <br> `"sin"(X)/(2) "sin"(Y)/(2) "sin"(Z)/(2) = (r)/(4R) = (sqrt((8)/(3)))/(4(35 sqrt6)/(24)) = (4)/(35)` <br> `sin^(2) ((X +Y)/(Z)) = cos^(2) ((Z)/(2)) = (1 + cos Z)/(2) = (3)/(5)` (Using cosine rule)Transcript

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00:00 - 00:59 | Alwar want to the question as in a triangle xyz xyz the length of the side opposite to the angles xyz respectively so as to ensure that I am trying the diagram this is basically the xyz and this is angle X and writing down here also this is angle action opposite asitis X this is angle by and this is opposite side b is angle then the opposite side set so evident as to the information given out the next question after this is there was given that two times as the semi perimeter is X + Y + Z is the standard to sirf I am given the condition that at minus x upon 4 is equal to 1 minus y + 3 is equal to 8.2 of incircle of the triangle x y z is it pi by 3 then we having four options the first is area of triangle xyz 2626 |

01:00 - 01:59 | S is the radius of circumcircle of the triangle xyz is 35686 she is sin x by 2 into 2 into sin Z by 2 is equal to four 137 4th sin square x + Y upon 2 is equal to 3.5 so we have to find out the values and then check with your options are correct or not sunao preceding we are given value of semi perimeter that is a tool that is this is 2S semi-perimeter given it is equal to X + Y + Z so also it is as - X upon 4 is equal to minus y point 4 is equal to minus 1 upon 2 is equal to Lambda this is that and this is this is equal to run by Amazon to be equal to Lambda breaches any constant so equating each and every portion |

02:00 - 02:59 | S - x is equal to four Lambda as minus Y is equal to four Lambda and S - Z is equal to 2 Lander now solving this what I get I get a reading this I get 3S minus x + Y + Z is equal to 9 lamp time using this thing that it's my pleasure it's good to ISI gets treatment with that is as is equal to 9 Now since we know the value of the rest then we can find out xyz week if x is equal to Y is equal to 6 cm and Z is equal to 7 |

03:00 - 03:59 | now we know that area is bi R square so it is so this is our this is equal to it is given as equal to 8 bye-bye Lambda in the question super Kansas with fire wicket R square is equal to 8 upon Lambda now I'm finding the area around to Delta would be equal using the herons formula so it is under the root of X into x minus x into x minus y into S - Z Delta is equal to under root of Amazon S9 Lambda 26634 Lambda |

04:00 - 04:59 | into three Lambda is 22 lamp that comes out with Lambda now let's find the Ash now let's find out are so are would be equal to X Y Z upon 4 times delta H is the radius of the circumcenter of triangle substituting the value get fired Lambda is 26 Lambda in 27 Lambda upon area that is root 6 Lambda is cancelled with this India left with 35 upon 4 root 6 into the value of are now using Lambda School 2115 lamp equal to 1 what I get let's look at the optimal one area would be cool to 626 the second was the radius of the in circle so |

05:00 - 05:59 | radius of circumcircle of the radius of the circle are equal to 35 upon 4 root option Embassy to option of Bsc with we had to find it hard to find ok h r is equal to 4 hour time X upon 2 X upon 2 Prime of Z upon 2 so that with is equal to 2 root 2 upon under root of things after the values it is 4 into 35.4 root 6 into sin x by 2 Sin bye-bye tools |

06:00 - 06:59 | now it becomes for upon which is equal to sin x by 2 X by 2 and Science that buy-to-let have a look at the option of it that is sin square x + b upon to so it would be equal to cos square that 52 substituting the values it is a minus b upon x square is the value it is 92 upon 5 it is it this is call amru equal to 1 this which of the following options are detector option so you can see a correct is that can disconnect a c and d are the correct option I hope IT Solutions Kiya thank you |