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

Sum

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

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APPEARS IN

Samacheer Kalvi Mathematics Class 10 SSLC Tamil Nadu State Board
Chapter 4 Geometry
Unit Exercise – 4 | Q 4 | Page 200
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