PROBLEMS ON INTERSECTING SECANT THEOREM

Problem 1 :

intersect-q1

Solution:

As per angle of intersecting secant theorem,

∠QSE=QS-RT24x-2=155-(-6+7x)24x-2=155+6-7x24x-2=161-7x2

8x - 4 = 161 - 7x

8x + 7x = 161 + 4

15x = 165

x = 165/15

x = 11

Problem 2 :

intersect-q2

Solution:

According to angle of intersecting secant theorem,

9x-3=36x+15-(19x+15)29x-3=36x+15-19x-1529x-3=17x217x=18x-617x-18x=-6-x=-6x=6

Problem 3 :

intersect-q3

Solution:

According to angle of intersecting secant theorem,

∠MKJ=(MJ-LJ)250=19x+13-8x-1219x+13-8x-1=10011x+12=10011x=100-1211x=88x=8

Problem 4 :

intersect-q4

Solution:

According to angle of intersecting secant theorem,

∠FDC=CF-CE230x=118x-1-57230x=118x-58260x=118x-58118x-60x=5858x=58x=1

Problem 5 :

intersect-q5.png

Solution:

According to angle of intersecting secant theorem,

∠BAC=BC-DE2x=125-272x=982x=49

Problem 6 :

intersect-q6.png

Solution:

According to angle of intersecting secant theorem,

∠ABC=AC-AD2x=200-402x=1602x=80

Problem 7 :

intersect-q7

Solution:

∠ABC=AC-DE230=5x+10-3x-4)230=2x+6260=2x+62x=54x=27

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