# AB and CD intersect at point O, AO = 12cm, BO = 4cm, CO = 30cm, DO = 10cm.

October 3, 2021 | education

| **AB and CD intersect at point O, AO = 12cm, BO = 4cm, CO = 30cm, DO = 10cm. Find Angle CAO if Angle DBO = 61degree**

The ratio of the lengths of the segments OS / OD and OA / OB is the same.

OS / OD = 30/10 = 3.

ОА / ОВ = 12/4 = 3.

FOD angle = AOC as vertical angles.

Then the FOD triangle and AOD are similar in two proportional sides and the angle between them with a similarity factor of 3.

The segments ВD and АС, ОВ and ОА have similar sides, then the angle DВО = САО = 61.

Answer: Angle DBO is 610.

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