If CD=15,DB=9, AD bisects ∠A, ∠ABC=90∘, then AB has length
32
18
7
24
A
18
B
7
C
24
D
32
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Solution
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Let ∠DAB=θ
⇒∠CAB=2θ
Let AB=x
tan2θ=24x and tanθ=9x
⇒2tanθ1−tan2θ=24x
⇒18x1−81x2=24x
⇒1−81x2=34
⇒x2=324
⇒x=18
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