In the given figure, AP is angle bisector of ∠CAE, CP = 7 cm and PE = 8 cm. find the length of AB
(a) 32
(b) 25
(c) 49
(d) 56
Sol:
∠BAC = ∠CEA,
In ∆ABC and ∆ABE, AE = 4x, AC = 3.5x
∆ABC ~ ∆ABE
∠B = common.
BC/AB=AC/AE
BC/AB=3.5X/4X
(AB)² = (BC) × (BE)
(4x)² = (3.5x) (3.5x + 15)
16x² = 3.5x (3.5x + 15)
7.5x = 15 × 7
x = 15 × 7/7.5
AB = 4 × 14
= 56 cm
