ABC is an isosceles triangle with …
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Naveen Sharma 7 years, 1 month ago
Ans.
Given: ABC is isosceles triangle. AB = AC. D is mid-point of AC.
To prove : {tex}AE = {1\over 4}AC{/tex}
Proof:
AB = AC …………(1) (Given)
AD = AC/2 ……………(3) (d is midpoint)
As AD is tangent to the triangle and AEB is secant then,
{tex}=> AE \times AB = AD^2{/tex}
{tex}=> AE \times AC = ({AC\over 2})^2{/tex}
{tex}=> AE \times AC = {AC^2\over 4}{/tex}
{tex}=> AE = {AC\over 4}{/tex}
Hence Proved.
3Thank You