ln the given figure AC is the tangent to the at point B. ∆EFD is an equilateral triangle and angle CBD is 40° . Find

February 2023 1 4 Report

ln the given figure AC is the tangent to the at point B. ∆EFD is an equilateral triangle and angle CBD is 40° . Find angle BFD., angleFBD. ,angleABF

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Question

In the given figure, AC is a tangent to the circle with centre 0. If ∠ADB=550, find x and y. Give reasons for your answers.

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Solution

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We know that angle between the radius and the tangent at the point of contact is right angle.

∠A=900

Also, in ΔOBE,OB=OE=radius(r)

In ∠B=∠OEB

In ΔABD,

∠A+∠B+∠ADB=1800

900+∠B=550=1800

∠B=1800−900−550=350

∠B=∠OEB=350

∠OEB=∠DEC=350 [vertically opp. ∠s]

∠EDC+∠ADE=1800

∠EDC+550=1800

∠EDC=1800−550=1250

In ΔEDC,

∠DEC+∠EDC+x=180