1957 AHSME Problems/Problem 46
Problem
Two perpendicular chords intersect in a circle. The segments of one chord are 
and 
;
the segments of the other are 
and 
. Then the diameter of the circle is:
Solution
![[asy] import geometry; point A = (0,0); point B = (6,3); point C = (8,0); point D, P; circle c = circumcircle(A,B,C); // Triangle ABC w/ Circumcircle draw(triangle(A,B,C)); dot(A); label("A",A,W); dot(B); label("B",B,N); dot(C); label("C",C,E); draw(c); // Segment BD, Triangle ADC pair[] d = intersectionpoints(perpendicular(B,line(A,C)),c); D = d[0]; dot(D); label("D",D,S); draw(B--D); draw(triangle(A,D,C)); pair[] p = intersectionpoints(B--D,A--C); P = p[0]; dot(P); label("P",P,SW); // Right angle mark markscalefactor = 0.0577; draw(rightanglemark(A,P,B)); // Length Labels label("$3$", midpoint(B--P), W); label("$4$", midpoint(P--D), W); label("$6$", midpoint(A--P), S); label("$2$", midpoint(P--C), S); [/asy]](http://latex.artofproblemsolving.com/8/b/d/8bd59c69fecdc4a648032b82fc852abf7137eb70.png)
.
See Also
| 1957 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 45 |
Followed by Problem 47 | |
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