Given the following diagram. (a) Name the radii _____________. Name the tangents ________________. (b) If given that AC is 6 cm and AE is 14, what is DE? Show all work or no credit. Answer:
Accepted Solution
A:
ANSWERai) AC and ADaii) CE and DEb) 4√10cmEXPLANATIONai)The center of the circle is A. The radius is the distance from the center to any point on the circumference.The radii are AC and AD.aii) The tangent to a circle touches the circle at only one point.The tangents to the circle are DE and CE.c) The radius is perpendicular to the tangents.This means thatTriangle ADE is a right triangle.[tex]|DE|^2+|AD|^2=|AE|^2[/tex]If AC is 6cm then AD is also 6cm.We substitute the values to obtain,[tex]|DE|^2+6^2=14^2[/tex][tex]|DE|^2=196 - 36[/tex][tex]|DE|^2=160[/tex][tex]|DE|= \sqrt{160} [/tex][tex]|DE|^2=4 \sqrt{10} cm[/tex]