Math, asked by deeksha8855, 10 months ago

9. Fig. 1 consists of a circle C with centre O. OA and OB are perpendicular to each other. The area of the triangle AOB is 32 square units. If AD = BD, the area of the triangle ABD is Fig.1 D A B O

Answers

Answered by amitnrw
7

32√2 + 32    or       32√2 - 32 cm² is area of ΔABD

Step-by-step explanation:

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 = 4√2   ( as OM² = OA² - AM²)

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

DM ⊥ AB

DM = DO + OM    or   DO - OM  ( depending on position of D)

DO = Radius = 8 cm

DM = (8 + 4√2)  or (8 - 4√2)

Area of ΔABD = (1/2) AB * DM

= (1/2) (8√2) (8 + 4√2)     or (1/2) (8√2) (8 - 4√2)

= 32√2 + 32    or      32√2 - 32

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