Question

(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

a) Radii: AC , AD

Tangents: DE, CE

b) 4sqrt(10)

Explanation:

ADE is a right angle triangle

14² = 6² + DE²

DE² = 160

DE = 4sqrt(10)

Answer 2

Part a) The radii are AC and AD and the tangents are CE and DE

Part b)
`DE=4√(10)\ cm`

Explanation:

Part a) we know that

The radius of a circle is the distance from the center of the circle to any point on the circle

A tangent to a circle is a straight line which touches the circle at only one point

so

In this problem

The radii are AC and AD

The tangents are CE and DE

Part b) If given that AC is 6 cm and AE is 14, what is DE?

we know that

The triangle ADE is a right triangle , because the radius AD is perpendicular to the tangent DE

Applying the Pythagoras Theorem

`AE^(2)= AD^(2)+DE^(2)`

we have

`AD=AC=6\ cm` -----> is the radius of the circle

`AE=14\ cm`

substitute and solve for DE

`14^(2)= 6^(2)+DE^(2)`

`DE^(2)=196-36`

`DE^(2)=160`

`DE=√(160)=4√(10)\ cm`