Question

A rectangle abcd is inscribed in a circle with centre o its diagonal ca extends to point e outside the circle. On point d of circle ed is a tangent such that ac=2bc find angle dec

Answer 1

∠ DEC =30° if A rectangle abcd is inscribed in a circle   ca extends to point e outside the circle.  ed is tangent ac = 2bc  

Step-by-step explanation:

ac = 2bc

=> Sin ∠CAB  =  BC/AC

=> Sin ∠CAB = BC/2BC

=> Sin ∠CAB = 1/2

=> ∠CAB = 30°

∠BAD = 90°  Rectangle

∠DAC = ∠BAD  - ∠CAB

=> ∠DAC = 90° - 30°

=> ∠DAC = 60°

=> ∠DAO = 60°

in Δ DAO

OA = OD ( Radius)

=> ∠ADO = 60°

=> ∠AOD  = 60°

=> ∠EOD  = 60°

∠EDO = 90°   ( ED is tanegnt)

Δ  in DOE

∠EOD + ∠EDO + ∠ DEO = 180°

=> 60° + 90° +   ∠ DEO = 180°

=>  ∠ DEO =30°

=> ∠ DEC =30°

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