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Question

In the adjoining figure, find the length of AD in terms of b and c.
1051860_442ba84233ba4c12a97b66f24f4a6fd2.png

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Solution

In ΔBAC,


BC2=AC2+AB2


BC2=b2+c2


BC=b2+c2


Now, in ΔABD and ΔCBA,


B=B (common)


ADB=BAC (each 90)


So, by AA similarity,


ΔABDΔCBA


Since the corresponding parts of similar triangles are similar, then,


ABCB=ADAC


cb2+c2=ADb


AD=bcb2+c2


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