## Search found 73 matches

Sat Jan 21, 2017 5:33 pm
Forum: Junior Level
Topic: Dhaka '15 \10
Replies: 3
Views: 2111

### Re: Dhaka '15 \10

Let BC and DF (Extended) meet at point Q. AE:ED=1:3, AE:AD=1:4, ED:AD=3:4 BF:AF=1:7, BF:AB=1:8, AF:AB=7:8 ∠FQB=∠DQC, BF||CD and ∠BFQ=∠CDQ. So, ΔBFQ~ΔCDQ, BQ/CQ = BF/CD = 1:8 ΔBFQ~ΔAFD, BF/AF = BQ/AD = 1/7 (BQ/AD) × (AD/ED) = 1/7 × 4/3 or, BQ/ED = 4/21 (BC/ED) + (BQ/ED) = 4/3 + 4/21 or, (BC+BQ)/ED = ...
Fri Jan 20, 2017 8:46 am
Forum: Junior Level
Topic: Dhaka '15 \10
Replies: 3
Views: 2111

### Re: Dhaka '15 \10

Capture.JPG Let DF and BC (Extended) meet at point Q. FB:AB=1:7, FB:CD=1:8. AE:ED=1:3, AD:ED=4:3. Between ΔDQC and ΔFQB, ∠Q is common and ∠BFQ=∠CDQ as AB||CD and QD is bisector. So, ΔDQC~ΔFQB. Then, FB:CD=QB:QC=1:8 ∠QFB=∠AFD, AD||BC||QC, ∠ADF=∠FQB, ΔAFD~ΔBFQ. QB:AD=BF:AF=1:7. QB/AD × AD/ED= 1/7 × 4...
Thu Jan 19, 2017 9:26 pm
Forum: Junior Level
Topic: BDMO 2013 QUE-9
Replies: 5
Views: 2724

### Re: BDMO 2013 QUE-9

Is ther any problem here? We assume two integers: (a,b) where, a=x×y and, b=y×z, such that: gcd(x,z)=1 and y is the GCD of these two integers. So, the sum is: (a+b)=(x×y)+(y×z)=y(x+z)=5460 and, differnece: (a-b)=(x×y)-(y×z)=y(x-z) So, gcd(a,b)=y and, lcm=(a,b)=x×y×z. Then, lcm(a,b)/gcd(a,b) = 36/1 [...