O āĻā§āύā§āĻĻā§āϰā§āϝāĻŧ āĻŦā§āϤā§āϤā§āϰ AB āĻŦā§āϝāĻžāϏāĨ¤ A āĻŦāĻŋāύā§āĻĻā§ āĻĻāĻŋāϝāĻŧā§ āĻ
āĻā§āĻāĻŋāϤ āĻāĻāĻāĻŋ āϏāϰāϞāϰā§āĻāĻž āĻŦā§āϤā§āϤāĻā§ C āĻŦāĻŋāύā§āĻĻā§āϤ⧠āĻāĻŦāĻ B āĻŦāĻŋāύā§āĻĻā§āϤ⧠āĻ
āĻā§āĻāĻŋāϤ āϏā§āĻĒāϰā§āĻļāĻāĻā§ D āĻŦāĻŋāύā§āĻĻā§āϤ⧠āĻā§āĻĻ āĻāϰā§āĨ¤ āĻĒā§āϰāĻŽāĻžāĻŖ āĻāϰāĻŋ āϝā§, BD\(^2\)=AD.DC
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āϧāϰāĻŋ,O āĻā§āύā§āĻĻā§āϰā§ā§ āĻŦā§āϤā§āϤā§āϰ AB āĻŦā§āϝāĻžāϏāĨ¤ A āĻŦāĻŋāύā§āĻĻā§ āĻĻāĻŋā§ā§ āĻ
āĻā§āĻāĻŋāϤ
āĻāĻāĻāĻŋ āϏāϰāϞāϰā§āĻāĻž āĻŦā§āϤā§āϤāĻā§ C āĻŦāĻŋāύā§āĻĻā§āϤ⧠āĻāĻŦāĻ B āĻŦāĻŋāύā§āĻĻā§āϤā§
āĻ
āĻā§āĻāĻŋāϤ āϏā§āĻĒāϰā§āĻļāĻāĻā§ D āĻŦāĻŋāύā§āĻĻā§āϤ⧠āĻā§āĻĻ āĻāϰā§āĻā§āĨ¤ āĻĒā§āϰāĻŽāĻžāύ āĻāϰāϤā§
āĻšāĻŦā§ āϝā§, BD\(^2\)=AD.DC
āĻ
āĻā§āĻāύāĻ B,C āϝā§āĻā§āϤ āĻāϰāĻž āĻšāϞāĨ¤
āĻĒā§āϰāĻŽāĻžāύāĻ āϝā§āĻšā§āϤ⧠â ACB=1 āϏāĻŽāĻā§āĻŖ[āĻ
āϰā§āϧāĻŦā§āϤā§āϤāϏā§āĻĨ āĻā§āĻŖ]
â´âACB āϏāĻŽāĻā§āĻŖā§ āϤā§āϰāĻŋāĻā§āĻāĨ¤
āĻāĻŦāĻžāϰ,AB āĻŦā§āϝāĻžāϏā§āϰ B āĻŦāĻŋāύā§āĻĻā§āϤ⧠BD āϏā§āĻĒāϰā§āĻļāĻ,āϏā§āϤāϰāĻžāĻ
â ABD=1 āϏāĻŽāĻā§āĻŖāĨ¤
â´âABD āĻāĻāĻāĻŋ āϏāĻŽāĻā§āĻŖā§ āϤā§āϰāĻŋāĻā§āĻāĨ¤
āĻāĻŦāĻžāϰ,âABD āĻāϰ āϏāĻŽāĻā§āύāĻŋāĻ āĻŦāĻŋāύā§āĻĻā§ B āĻĨā§āĻā§
āĻ
āϤāĻŋāĻā§āĻ AD āĻāϰ āĻāĻĒāϰ BC āϞāĻŽā§āĻŦāĨ¤
â´âABD āĻ âBCD āϏāĻĻā§āĻļ
â´ \(\frac{BD}{AD}=\frac{DC}{BD}\)
āĻŦāĻž, BD\(^2\)=AD.DC [āĻĒā§āϰāĻŽāĻžāύāĻŋāϤ]
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