You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Tangent Secant Theorem

AB = AC, D is...

Question

$A B = A C, D$ is the mid point of $A C, B D$ is the diameter of circle, than prove that $A E = \frac{1}{4} A C$ .

Open in App

Solution

We have to prove $A E = \frac{1}{4} A C$
So from figure According to tangent Secant theorum
$A D^{2} = A E \times A B$ [Here $A D = t a n g e n t$ ]
$A B = S e c a n t$
$A E = \frac{A D^{2}}{A B}$
As we know's 'D' is mid point
$= \frac{(\frac{A C}{2})^{2}}{A B}$ $[A D = \frac{A C}{2}]$
And we know
$\frac{A C^{2}}{4 * A C}$ $[A B = A C]$
$A E = \frac{1}{4} A C$

Suggest Corrections

Similar questions

A B C

is an isosceles triangle such that

A B = A C

D

is the mid point of

A C

. A circle is drawn taking

B D

as diameter which intersects

A B

at point

E

.then

A C = 3 A E

AB is a diameter and AC is chord of a circle with centre O such that $∠ B A C = 30^{\circ}$ . The tangent at C intersects AB at a point D. Prove that BC =BD.

A B

is a diameter and

A C

is a chord of a circle with centre

O

such that

∠ B A C = 30^{o}

. The tangent at

C

intersects

A B

at a point

D

. Prove that

B C = B D

Q. AB is the diameter and AC is a chord of a circle such that

B A C = 30^{\circ}

. If tangent at C intersects AB produced in D, prove that BC=BD.

Q. AB is a diameter and AC is a chord of a circle with centre O such that angle BAC = 30°. The tangent at C intersects extended AB at a point D. Prove that BC=BD.

Join BYJU'S Learning Program

AB=AC,D is the mid point of AC,BD is the diameter of circle, than prove that AE=14AC.

We have to prove AE=14ACSo from figure According to tangent Secant theorumAD2=AE×AB [Here AD=tangent] AB=SecantAE=AD2AB As we know's 'D' is mid point=(AC2)2AB [AD=AC2] And we knowAC24∗AC [AB=AC]AE=14AC

$A B = A C, D$ is the mid point of $A C, B D$ is the diameter of circle, than prove that $A E = \frac{1}{4} A C$ .