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

Construction of Tangent from a Point Outside Circle

Which of the ...

Question

Which of the following is true if $A B C$ is a triangle in which $A B = A C$ and a circle through $B$ touches $A C$ at $D$ and intersects $A B$ at $P$ . If $D$ is the midpoint of $A C$

A P = A B

No worries! We‘ve got your back. Try BYJU‘S free classes today!

A B = 2 A P

No worries! We‘ve got your back. Try BYJU‘S free classes today!

A D = B D

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4 A P = A B

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $4 A P = A B$
$A C$ is tangent and $A P B$ is a secant to the circle.
$A P \times A B = A D^{2}$
$\Rightarrow A P \times A B = {(\frac{1}{2} A C)}^{2}$
$\Rightarrow A P \times A B = {(\frac{1}{2} A B)}^{2} . . . [A C = A B]$
$\Rightarrow 4 A P = A B$

Suggest Corrections

Similar questions

Q. Draw a triangle

A B C

in which

A B = A C

and a circle through

B

touches

A C

D

and intersect

A B

P

, if

D

is the mid-point of

A C

, then prove that

A B = 4 A P

Q. ABC is an isosceles triangle in which AB = AC A circle through B touches side AC at its mid point D and intersects AB at P, then AP will be-

△ A B C

is isosceles with AB = AC. If a circle through B touches the side AC at its mid-point D and intersects the side AB at P, then find the value of

\frac{A P}{A B}

$△ A B C$ is isosceles with AB = AC. If a circle through B touches the side AC at its mid-point D and intersects the side AB at P, then $\frac{A P}{A B}$ = ______.

Q. In an isosceles triangle

A B C, A B = A C

. A circle passing through

B

and touching

A C

at its middle point D, intersects

A B

M

. If

A M = 3 c m

, then

A B = . . . .

Join BYJU'S Learning Program

Which of the following is true if ABC is a triangle in which AB=AC and a circle through B touches AC at D and intersects AB at P. If D is the midpoint of AC

The correct option is D 4AP=ABAC is tangent and APB is a secant to the circle.AP×AB=AD2⇒AP×AB=(12AC)2⇒AP×AB=(12AB)2...[AC=AB]⇒4AP=AB

Which of the following is true if $A B C$ is a triangle in which $A B = A C$ and a circle through $B$ touches $A C$ at $D$ and intersects $A B$ at $P$ . If $D$ is the midpoint of $A C$

The correct option is D $4 A P = A B$
$A C$ is tangent and $A P B$ is a secant to the circle.
$A P \times A B = A D^{2}$
$\Rightarrow A P \times A B = {(\frac{1}{2} A C)}^{2}$
$\Rightarrow A P \times A B = {(\frac{1}{2} A B)}^{2} . . . [A C = A B]$
$\Rightarrow 4 A P = A B$