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okay to whoever helps me witth these I thank you greatly smiley

 

The side lengths of a cyclic quadrilateral ABCD are provided in the diagram. Find \(BD^2\)

 

[asy]
size(150);

pair A,B,C,D;

A=dir(10);
B=dir(46);
C=dir(118);
D=dir(210);

draw(D--A--B--C--D--B);
draw(circle(origin,1),blue);

dot("$A$",A,A);
dot("$B$",B,B);
dot("$C$",C,C);
dot("$D$",D,D);

label("$1$",A--B,-(A+B)/2);
label("$2$",B--C,-(B+C)/2);
label("$3$",C--D,(C+D)/2);
label("$4$",D--A,(D+A)/2);

[/asy]

 Jun 22, 2022
 #1
avatar
0

By Ptolemy, BD^2 = 63/5.

 Jun 22, 2022

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