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$A circle is touching the side PQ of a /_\APQ at E and touching the side AP and AQ produced at B and C respectively. If AB=5cm, then find the perimeter of /_\APQ.$

A circle is touching the side $P Q$ of a $\triangle A P Q$ at $E$ and touching the side $A P$ and $A Q$ produced at $B$ and $C$ respectively. If $A B=5 \mathrm{~cm}$ , then find the perimeter of $\triangle A P Q$ .

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Convert equations of circles from general to standard form

Full solution

Q. A circle is touching the side

P Q

of a

\triangle A P Q

at

E

and touching the side

A P

and

A Q

produced at

B

and

C

respectively. If

A B=5 \mathrm{~cm}

, then find the perimeter of

\triangle A P Q

.

Identify Circle Properties: Identify the properties of the circle touching the triangle sides. $\newline$ Since the circle touches $PQ$ at $E$ and extends to touch $AP$ and $AQ$ at $B$ and $C$ , respectively, $AB = BC = CA = 5\,\text{cm}$ (as the circle's radius is equal to each segment due to tangency).
Calculate Triangle Perimeter: Calculate the perimeter of triangle $APQ$ . Perimeter of triangle $APQ = AB + BP + PQ + QE + EA$ Since $AB = BC = CA = 5 \, \text{cm}$ , and $BP = PC$ , $PQ = QE = EA$ (as tangents from a point outside a circle to the circle are equal).

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