Triangle BAD is right-angled at B. On AD there is a point C for which AC=CD and AB=BC. The magnitude of angle DAB, in degrees, is:

1963 AMC 12 Problem 6

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Triangle

BAD

is right-angled at

B.

AD

there is a point

C

for which

AC=CD

and

AB=BC.

The magnitude of angle

DAB,

in degrees, is:

67\dfrac12

60

45

30

22\dfrac12

A midpoint of a right triangle’s hypotenuse is equidistant from all three vertices

Use

AB=BC=AC

Since

C

is the midpoint of hypotenuse

AD,

AC=BC=CD.

Given

AB=BC,

triangle

ABC

is equilateral. Thus

\angle DAB=\angle CAB=60^\circ.

Therefore, the correct answer is B.