A andy849 New member Joined Jan 31, 2010 Messages 4 Feb 2, 2010 #1 In a diagram of circle, chords AB and CD intersect at E. If AE = 3, EB = 4, CE = x, and ED = x - 4, what is the value of x? how do I start this problem?
In a diagram of circle, chords AB and CD intersect at E. If AE = 3, EB = 4, CE = x, and ED = x - 4, what is the value of x? how do I start this problem?
S soroban Elite Member Joined Jan 28, 2005 Messages 5,584 Feb 2, 2010 #2 Hello, andy849! \(\displaystyle \text{In a diagram of a circle, chords }AB \text{ and }CD\text{ intersect at }E.\) \(\displaystyle \text{If }\,AE \,=\, 3,\; EB \,=\, 4,\; CE \,=\, x,\;ED \,=\, x - 4,\,\text{ what is the value of }x\,?\) Click to expand... Theorem: If two chords intersect inside a circle, the products of their segments are equal. \(\displaystyle \text{So we have: }\;x(x-4) \:=\:3\cdot4 \quad\Rightarrow\quad x^2 - 4x - 12 \:=\:0\) \(\displaystyle \text{Hence: }\;(x-6)(x+2) \:=\:0 \quad\Rightarrow\quad x \:=\:6,\;\rlap{\;///}-2\) \(\displaystyle \text{Therefore: }\:x \,=\,6\)
Hello, andy849! \(\displaystyle \text{In a diagram of a circle, chords }AB \text{ and }CD\text{ intersect at }E.\) \(\displaystyle \text{If }\,AE \,=\, 3,\; EB \,=\, 4,\; CE \,=\, x,\;ED \,=\, x - 4,\,\text{ what is the value of }x\,?\) Click to expand... Theorem: If two chords intersect inside a circle, the products of their segments are equal. \(\displaystyle \text{So we have: }\;x(x-4) \:=\:3\cdot4 \quad\Rightarrow\quad x^2 - 4x - 12 \:=\:0\) \(\displaystyle \text{Hence: }\;(x-6)(x+2) \:=\:0 \quad\Rightarrow\quad x \:=\:6,\;\rlap{\;///}-2\) \(\displaystyle \text{Therefore: }\:x \,=\,6\)
