Question

Chords AB and CD intersect at right angle .If ∠BAC=40 then∠ ABD is- 

40°

30°

50°

45°

​

Answer 1

The correct answer is 50°

GIVEN

Chords AB and CD intersect at right angle. ∠BAC = 40°

TO FIND

∠ABD

SOLUTION

Please refer to the picture

We can simply solve the above problem as follows;

Let the point of intersection of the chord be 'O'.

∠AOC = 90°

Therefore,

In ΔAOC

∠AOC + ∠OAC + ∠ACO = 180°

90 + 40 + ∠ACO = 180

∠ACO = 180- 130 = 50°

Now,

AO :CO = 5:4 [since larger angle denotes shorter length]

Therefore,

Ratio of-

OB:OD=4:5 [ since they intersect and ratio gets changed]

or,

∠OBD:∠ODB=5:4 [larger length has smaller ratio]

Therefore,

∠OBD+∠ODB+90=180

5x + 4x + 90 = 180

9x + 90 = 180

x + 10 = 20

x = 10

∠OBD = 5 × 10 = 50°

Since,

∠OBD = ∠ABD

Therefore,

∠ABD = 50°

Hence, The correct answer is 50°

#SPJ1