Problem:AB is a diameter of a circle. Tangents AD and BC are drawn so that AC and BD intersect in a point on the circle. If AD=a and BC=b,aξ =b, the diameter of the circle is:
Answer Choices:
A. β£aβbβ£
B. 21β(a+b)
C. abβ
D. a+babβ
E. 21βa+babβ
Solution:
From similar triangles yxβ=daβ and dβyxβ=dbβ
β΄y(dβy)x2β=d2abβ. But x2=y(dβy).β΄1=d2abββ΄d=abβ.
OR
Let the degree measure of arc AP be m.
Then β D=90β2mβ and β C=2mβ.
β΄bdβ=tan2mβ and adβ=tan(90β2mβ)=tan2mβ1β
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