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In Fig., altitudes AD and CE of triangle...

In Fig., altitudes AD and CE of `triangleABC` intersect each other at the point P. Show that:
(i) `triangleAEP ~ triangleCDP`
(ii) `triangleABD ~ triangleCBE`
(iii) `triangleAEP ~ triangleADB`
(iv) `trianglePDC ~ triangleBEC`

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