Question 7The tangents to the circumcircle of an isosceles -ABC at A- which AB-AC- is parallel to BC-

True Let EAF be tangents to the circumcircle of ∆ABC To prove: EAF ∥ BC Here, AB =AC ⇒∠ ABC = ∠ ACB ...(i) [Base angles of an isosceles triangle are equal] ...

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Standard X

Mathematics

Tangents from a Given Point

Question 7The...

Question

Question 7
The tangents to the circumcircle of an isosceles $Δ$ ABC at A, which AB=AC, is parallel to BC.

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Solution

True
Let EAF be tangents to the circumcircle of ∆ABC

To prove: EAF $∥$ BC
$H e r e, A B = A C \Rightarrow ∠ A B C = ∠ A C B . . . (i)$
[Base angles of an isosceles triangle are equal]
Angle between a tangent and a chord is equal to the angle made by chord in the alternate segment.
$∴ ∠ E A B = ∠ B C A . . . (i i)$
From Eqs. (i) and (ii), we get
$∠ E A B = ∠ A B C \Rightarrow E A F ∥ B C$
( Since, the alternate interior angles are equal)

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Similar questions

Q. Write True or False:

The tangent to the circumcircle of an isosceles

△ A B C

at A, in which

A B = A C

, is parallel to BC.

If $△ A B C$ is isosceles with AB = AC, prove that the tangent at A to the circumcircle of $△ A B C$ is parallel to BC. [2 MARKS]

Q. In the given figure,

P A T

is a tangent to the circumcircle of a

Δ A B C

at the vertex

A

. A line parallel to

P A T

intersects the sides

A B

and

A C

at the points

D a n d E

respectively.
Prove that

Δ A B C \sim Δ A E D

A B \cdot A D = A C \cdot A E

Question 2
In $Δ A B C, A D$ is the perpendicular bisector of BC (see the given figure).
Show that $Δ A B C$ is an isosceles triangle in which AB = AC.

Q. Tangent at

P

to the circumcircle of triangle

P Q R

is drawn. If this tangent is parallel to side

Q R

show that

△ P Q R

is an isosceles triangle.

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Question 7 The tangents to the circumcircle of an isosceles ΔABC at A, which AB=AC, is parallel to BC.

Question 7
The tangents to the circumcircle of an isosceles $Δ$ ABC at A, which AB=AC, is parallel to BC.