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Given a triangle with unequal sides, if P is the set of all points which are equidistant from B and C, and Q is the set of all points which are equidistant from sides AB and AC, then what is the P intersection with Q equal to?

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answer is A.

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Detailed Solution

Since, the

⊥

bisector of BC obeys the laws of a point that is equally distant from B and C.
The angular bisector between two lines is the locus of a point that is equally distant from two intersecting lines.
C:UserssoftberryDownloadsP0042 JPEGq8.jpg

C:UserssoftberryDownloadsP0042 JPEGq8.jpg

So,

⊥

bisector of BC will occasionally coincide with the angular bisector of the angle between AB and AC.

∴ n (P \cap Q) = 1

Option 1 is correct.

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