Question

If BD = 2.4 and AB = 1.0, calculate the value of DA. circle D with tangent line segment AC touching at point B; line segment AD 1.96 2.18 11.56 2.6

If AB = 9, CD = 12, and FE = 22, calculate the values of line segment AE and line segment CE
image of a circle inscribed inside triangle ACE; the points of intersection points are: on side AC point B, on side AE point F, and on side CE point D

AE = 34 and CE = 31

AE = 31 and CE = 34

AE = 21 and CE = 34

AE = 34 and CE =21

Answer 1

• 2.6
• AE = 31; CE = 34

Explanation:

a) Triangle ABD is a right triangle with side lengths 1 and 2.4. The triangle inequality requires hypotenuse AD have a length between 2.4 and 3.4. Only one answer choice is in that range: DA = 2.6.

(The ratio of the given sides is 1 : 2.4 = 5 : 12. These match the Pythagorean triple 5:12:13, so you know the hypotenuse DA is 2.6 units long. Even if you're not familiar with that triple, you can use the Pythagorean theorem to calculate the length of DA.)

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b) Tangents to a circle from the same point are the same length, so ...

FA = BA = 9

AE = FA +FE = 9 +22 = 31 . . . . . . sufficient to choose the correct answer

and ...

DE = FE = 22

CE = CD +DE = 12 +22 = 34

The side lengths are AE = 31, CE = 34.