+0  
 
0
115
1
avatar

1) A, B, C, and D are points on a circle, and segments AC and BD intersect at P, such that AP = 8, PC = 1, and BD = 6. Find BP, given that BP < DP.

 

2) In 4ABC, AB = 3 and BC = 5. Find the number of possible integer values of CA. [Disclaimer]: In this class, we do not consider degenerate triangles (i.e. a triangle whose area is 0).

 

3) In obtuse 4ABC, AB = 3 and BC = 5. Find the number of possible integer values of CA

 Mar 23, 2020
 #1
avatar+713 
+1

1) A, B, C, and D are points on a circle, and segments AC and BD intersect at P, such that AP = 8, PC = 1, and BD = 6. Find BP, given that BP < DP.

 

Let AC be a side of an inscribed square. Let O be a center of a circle, and N is the intersection point of BD and CO.

AP = 8       PC = 1        BD = 6        ∠(CPN) = 45°

 

PN = sqrt [(PC)² /2]  =  sqrt(1/2) [ sqrt(50)] /10  =  sin(45°) = cos(45°) = 0.707106781

 

BP = ( BD/2 ) - PN = 2.292893219 units   indecision

 

 Mar 23, 2020
edited by Dragan  Mar 23, 2020
edited by Dragan  Mar 23, 2020
edited by Dragan  Mar 24, 2020
edited by Dragan  Mar 24, 2020

34 Online Users

avatar
avatar
avatar
avatar