CameraIcon

SearchIcon

MyQuestionIcon

1

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

Sum of Pair of Opposite Angles in Quadrilateral

In the given ...

Question

In the given figure, a circle touches the side $P Q$ of a $△ A P Q$ at $R$ and side $A P$ and $A Q$ produced at the point $B$ and $C$ . show that $A B = \frac{1}{2}$ (Perimeter of $△ A P Q)$

Open in App

Solution

$B P = B Q$
$C P = C R$
$A Q = A R$
$A B + B Q = A C + C R$
$A B + B P = A C + C P$
$△ A B C = A B + B C + C A$
$A B + (B P + P C) + C A$ \\
$(A B + B P) (P C + C A)$
$2 (A B + B P) (A B + B P = A C + C P)$
$2 (A B + B Q) = 2 A Q$
$P Q = \frac{P E R I M E T E R O F △ A B C}{2}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. A circle touches the side BC of ∆ABC at P and touches AB and AC produced at Q and R, respectively, as shown in the given figure. Show that

A Q = \frac{1}{2} \times (perimeter of ∆ A B C) .

Q. In the given figure, a circle touches the side

B C

Δ A B C

P

A B

A C

Q

R

respectively. If

A Q = 5 c m

, find the perimeter of

Δ A B C

Q. In the figure, a circle touches the side BC of

△

ABC at P and sides AB and AC produced at Q and R respectively. What is the perimeter of

△

ABC if AQ = 5 cm?

Q. A circle touches the sides BC of a

Δ A B C

at P and touches AB and AC when produced at Q and R respectively as shown in the figure. Show that

A Q = \frac{1}{2}

Δ A B C

)
If true answer

^{'} 0^{'}

^{'} 1^{'}

Q. A circle touches the side

B C

△ A B C

P

A B

A C

Q

R

respectively. Prove that

A Q = \frac{1}{2}

△ A B C

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Circles and Quadrilaterals - Theorem 11

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Sum of Pair of Opposite Angles in Quadrilateral

Standard X Mathematics

Join BYJU'S Learning Program

CrossIcon