The chords of the circle AB and CD intersect at point P so that the angle APC = 90 degrees

The chords of the circle AB and CD intersect at point P so that the angle APC = 90 degrees, AP = 3, CP = 4, PD = 6. Find the length of the line segment DB.

By the property of intersecting chords of a circle, the product of the lengths of the segments formed at the intersection of one chord is equal to the product of the lengths of the segments of the other chord.

AP * BP = CP * DP.

3 * BP = 4 * 6.

3 * BP = 24.

BP = 24/3 = 8 cm.

Since, by condition, the chords intersect at right angles, the BPD triangle is rectangular.

Then, by the Pythagorean theorem, BD ^ 2 = BP ^ 2 + DP ^ 2 = 82 + 62 = 64 + 36 = 100.

ВD = 10 cm.

Answer: The length of the segment BD is 10 cm.