Question

in the given figure Of AP and AQ are tangents and AP =10 cm find the perimeter of triangle AXY​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

• AP, AQ and XY are tangents to a circle touches the circle at P, Q and R respectively.

Further,

• It is given that AP = 10 cm.

Now,

Consider,

$\rm :\longmapsto\:Perimeter _{(\triangle AXY)} = AX + AY + XY$

$\rm :\longmapsto\:Perimeter _{(\triangle AXY)} = AX + XY + AY$

$\rm :\longmapsto\:Perimeter _{(\triangle AXY)} = AX + XR + RY + AY$

$\rm :\longmapsto\:Perimeter _{(\triangle AXY)} = AX + XQ + YP + AY$

$\red{\bigg \{ \because \: Length \: of \: tangents \: are \: equal\bigg \}}$

$\rm :\longmapsto\:Perimeter _{(\triangle AXY)} = AQ +AP$

$\rm :\longmapsto\:Perimeter _{(\triangle AXY)} = AP+AP$

$\red{\bigg \{ \because \: Length \: of \: tangents \: are \: equal\bigg \}}$

$\rm :\longmapsto\:Perimeter _{(\triangle AXY)} = 2AP$

$\rm :\longmapsto\:Perimeter _{(\triangle AXY)} = 2 \times 10$

$\bf :\longmapsto\:Perimeter _{(\triangle AXY)} = 20 \: cm$

Additional Information :-

1. Length of tangent drawn from external point to a circle are equal.

2. Radius and tangent are perpendicular to each other.

3. Tangents are equally inclined to the line segment joining the center and external point.

4. One and only one tangent can be drawn to a circle at a point.

5. A circle can have infinitely many tangents.