If chords AB and CD intersect at P inside a circle, which equation expresses the power of a point?

If chords AB and CD intersect at P inside a circle, which equation expresses the power of a point?

• A. PA × PC = PB × PD
• B. PA + PB = PC + PD
• C. PA × PB = PC × PD
• D. PA × PD = PB × PC

Answer: (C)

The power of a point with respect to a circle is being tested. For a point inside the circle, the product of the distances from the point to the endpoints of one chord through the point is the same as the product for any other chord through that point. So, if a line through P meets the circle at A and B, the product PA × PB equals the circle’s power at P. If another line through P meets the circle at C and D, then PC × PD equals the same power. Therefore PA × PB = PC × PD. This is the expression that captures the equal power along both chords. The other forms don’t reflect this constant product along lines through P.

The power of a point with respect to a circle is being tested. For a point inside the circle, the product of the distances from the point to the endpoints of one chord through the point is the same as the product for any other chord through that point. So, if a line through P meets the circle at A and B, the product PA × PB equals the circle’s power at P. If another line through P meets the circle at C and D, then PC × PD equals the same power. Therefore PA × PB = PC × PD. This is the expression that captures the equal power along both chords. The other forms don’t reflect this constant product along lines through P.