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Question

Question 10
AB is a diameter of a circle and AC is the chord such that BAC = 30. If the tangent at C intersects AB extended at D, then BC = BD.

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Solution

True
To prove, BC = BD

Join BC and OC
GivenBAC=30BCD=30
[ angle between tangent and chord is equal to angle made by chord in the alternate segment]
ACD=ACO+OCD=30+90=120[OCCD and OA=OC=radiusOAC=OCA=30InΔACD,CAD+ACD+ADC=180
[ Since sum of all interior angles of a triangle is 180]
30+120+ADC=180ADC=180(30+120)=30Now, in ΔBCD BCD=BDC=30BC=BD
[Since , sides opposite to equal angles are equal]






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