Question

in a circle with center O ,chord AB=chord AC. Chord AD cuts BC in E. If AC= 12 and AE= 8, then AD equals to==

Answer 1

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Answer 2

Value of AD is 18

Step-by-step explanation:

Line segment with end points lying at the circumference of circle is called chord.

$\angle ABE = \angle BDE$

• Because Equal chords subtend equal angles and AB = AC are equal chords given.

In △ABE & △ABD:

⇒∠EAB = ∠DAB  (common)

⇒∠ABE=∠BDE

△AEB∼△ABE

by A−A similarity

$\frac {AD}{AB} = \frac {AB}{AE}$

⇒ $\frac {AD}{12} = \frac {12}{8}$ (Because AB = AC = 12)

⇒ AD = 18