Let $Δ$ $A B C$ be an equilateral triangle. Let P be a point on minor arc AB of its circumcircle . Which of the following holds :

P C = 2 P B

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P C^{2} = P A^{2} + P B^{2}

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P A = P B + P C

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P C = P A + P B

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Solution

The correct option is B $P C = P A + P B$
Draw $P A, P B, P C$ . By Ptolemy's Theorem applied to quadrilateral $A P B C$ ,
we know that $P C \times A B = P A \times P B + P B \times A C$ .
Since, $A B = B C = C A = s$ , we divide both sides of the last equation by to get the result: $P C = P A + P B$ .

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Let Δ ABC be an equilateral triangle. Let P be a point on minor arc AB of its circumcircle . Which of the following holds :

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