The chords CD and AB of the circle intersect at point O, CO = 4cm, OD = 3cm. P (aos) = 9cm.

The chords CD and AB of the circle intersect at point O, CO = 4cm, OD = 3cm. P (aos) = 9cm. Calculate the chord length DB if you know that the length of the segment AO is three times less than the length of the segment OB.

Find BO and OA.
To intersect the chords of a circle:
CO * OD = ВO * AO;
ВO = 3AO = CO * OD = 4 * 3 = 3AO = 4 = 2 cm;
BO = 3AO = 3 * 2 = 6;
P = 9 – 4 – 2;
P = 3;
S = √ 4.5 * (4.5 – 4) * (4.5 – 2) * (4.5 – 3);
S = √ 4.5 * 0.5 * 2.5 * 1;
S = 3;
S = 1/2 * OC * AO * sin A = 3/4;
СOA = ВOD;
By the cosine theorem:
ВD² = ВO² + OD² = 6² + 3² = 45 – 24 = 21
ВD = 4.58.
Answer: ВD = 4.58.