Question

A

12 cm
a=
xcm
X
B
xcm
4 cm
Y
Diagram NOT
accurately drawn
The points B, C, Y and X lie on a circle.
AXY and ABC are straight lines.
AX = 12 cm
XY = x cm
AB = x cm
BC= 4 cm
Show that x² - 8x + a = 0 where a is a constant to be found.
(3 marks)

Answer 1

a = - 144

Explanation:

AXY AND ABC are secants to the circle

given two secants drawn from an external point to a circle , then the product of the measures of one secant's external part and that entire secant is equal to the product of the measures of the other secant's external part and that entire secant , that is

AB × AC = AX × AY ( substitute values )

x(x + 4) = 12(12 + x) ← distribute parenthesis

x²+ 4x = 144 + 12x ( subtract 12x from both sides )

x² - 8x = 144 ( subtract 144 from both sides )

x² - 8x - 144 = 0

in the form x² - 8x + a = 0

with a = - 144