Question

ABCD is a trapezium such that ABllCD and AB = 3cm.If the diagonals AC and BD intersect at O such that OA / OC = OB / OD = 1 / 2, then calculate DC




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Answer 1

Answer:

Given :

• ABCD is a trapezium
• BC || AD
• AB = 4 cm .
• If the diagonals AC and BD
• intersect at Ο such that AΟ/ΟC = DΟ/ΟB = 1/2

Now from the triangle ΔAOB and ΔCOD,

∠AOB = COD (vertically opposite angle)

AO/OC = DO/OB (Given)

from SAS congruent criterion,

ΔAOB ≅ ΔCOD

Now

AO/OC = BO/OD = AB/DC (since corresponding sides of similar traingles are preportional)

=> 1/2 = 4/DC

=> DC = 4 × 2

=> DC = 8 cm

Answer 2

Answer:

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