All four sides of quadrilateral ABCD touch a circle drawn inside it. $AB = 15$ cm, $BC = 8$ cm and $CD = 9$ cm. What is DA?

2 cmCorrect answerYour answer8 cmCorrect answerYour answer14 cmCorrect answerYour answer16 cmCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

From each vertex the two tangents to the circle are equal. Adding them up shows that opposite sides have equal sums: $AB + CD = BC + DA$ .
$15 + 9 = 8 + DA$ , so $DA = 16$ cm.

Worth noting

Opposite sides are not equal (that gives 8 cm); their SUMS are. 14 cm and 2 cm pair up the wrong sides.

Concept: Equal tangents: in a quadrilateral around a circle, AB + CD = BC + DA
Typical timeTypical: 70 s
Your timeYours: —

Ten questions from Lines, Triangles and Circles, at your own pace.

Ten questions from Lines, Triangles and Circles, at your own pace.

All four sides of quadrilateral ABCD touch a circle drawn inside it. AB=15AB = 15AB=15 cm, BC=8BC = 8BC=8 cm and CD=9CD = 9CD=9 cm. What is DA?