Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th

ABC is a triangle in which AB = AC. Points D and E are points on the side AB and AC respectively such that AD = AE. Show that the points B, C, E and D lie on a same circle - Mathematics

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ABC is a triangle in which AB = AC. Points D and E are points on the side AB and AC respectively such that AD = AE. Show that the points B, C, E and D lie on a same circle

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Solution

∠B = ∠C ...(Given AB = AC)

AD + DB = AE + EC

BD = EC ...(Given AD = AE)

DE parallel BC Since AEC is a straight line.

∠AED + ∠CED = 180°

∠CBD + ∠CED = 180°

Similarly of the opposite angles = 180°

∴ BCED is a cyclic quadrilateral

Concept: Thales Theorem and Angle Bisector Theorem

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Chapter 4: Geometry - Unit Exercise – 4 [Page 200]

Q 4 Q 3 Q 5

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Samacheer Kalvi Mathematics Class 10 SSLC Tamil Nadu State Board

Chapter 4 Geometry
Unit Exercise – 4 | Q 4 | Page 200

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ABC is a triangle in which AB = AC. Points D and E are points on the side AB and AC respectively such that AD = AE. Show that the points B, C, E and D lie on a same circle - Mathematics

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