Question

Two tangents AB and BC intersect at B. Another line DE intersects AB and BC at D and E such that

∠ADE = 150o and ∠DEC = 140o

. The radius of the first curve is 200 m and that of the second is

300 m. The chainage of B is 950 m. Calculate all data necessary for setting out the compound

curve.​

Answer 1

Answer:

In △OBC and △OAD

BC=DA ....... (Given)

∠OCB=∠ODA ....... (∵CB∥DA, so alternate opposite angles are equal)

∠OBC=∠OAD ...... (∵CB∥DA, so alternate opposite angles are equal)

∴△OBC≅△OAD (By ASA criterion)

Thus, CO=DO and BO=AO (By C.P.C.T.C.)

⇒ So, O is the midpoint of AB and CD.