Question

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:

Answer 1

ai) AC and AD

aii) CE and DE

b) 4√10cm

Step-by-step explanation

ai)

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 that

Triangle ADE is a right triangle.

`|DE|^2+|AD|^2=|AE|^2`

If AC is 6cm then AD is also 6cm.

We substitute the values to obtain,

`|DE|^2+6^2=14^2`

`|DE|^2=196 - 36`

`|DE|^2=160`

`|DE|= √(160)`

`|DE|^2=4 √(10) cm`