Question

in figure 1 a circle with Centre O.OA nd OB are perpendicular to each other,area of triangle AOB is 32 units,AB and CD are equals ,find the area of triangle ABD​

Answer 1

Answer:

where is point C in your diagram?

Answer 2

32√2 + 32 = 77.25 cm² is area of ΔABD

Step-by-step explanation:

Correction

AD = BD  ( instead of AB = CD)

OA = OB = Radius

Area of ΔAOB = (1/2) * OA * OB = 32

=> Radius * Radius = 64

=> Radius² = 8²

=> Radius = 8 cm

OA = OB = 8 cm

AB² = OA² + OB²

=> AB = 8√2 cm

Let say M is mid point of AB

then AM = BM  = 4√2

OM ⊥ AB  as OA = OB

OM = 4√2   ( as OM² = OA² - AM²)

AD = BD   => DM will pass through center of circle O

DM ⊥ AB

DM = DO + OM    

DO = Radius = 8 cm

DM = (8 + 4√2)

Area of ΔABD = (1/2) AB * DM

= (1/2) (8√2) (8 + 4√2)  

= 32√2 + 32

= 77.25 cm²

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