Chords AB and CD are drawn in circle O. OE ⊥ AB, and OF ⊥ CD, point E being on AB and point F being on CD. If AB = CD, OE = 4x – 5, and OF = 3x + 6, find OE.

Answer 1

First of all, draw a diagram.

Since OE is perpendicular to chord AB, E bisects AB. Similarly, F bisects CD.

Since AB = CD and E and F are respective bisectors, EB = FC

Draw radii OB and OC.

Since any two radii of a given circle have the same length, OB = OC.

ΔOEB and ΔOFC are congruent by Hypotenuse Leg Theorem.

Since corresponding parts of congruent triangles are congruent, OE = OF

So, 4x - 5 = 3x + 6. Therefore, x = 11. So, OE = 39