Question

In the figure, the circle touches the sides of the quadrilateral PQRS at A, B, C and D.
PA=5 centimetres, QB = 4 centimetres, RC =3 centimetres, SD = 2 centimetres.
(a) What is the length of PD ?
(b) Find the perimeter of the quadrilateral PQRS,​

Answer 1

Given:

• A circle touches the sides of a quadrilateral PQRS at point A, B, C and D.
• PA = 5 cm, QB = 4 cm, RC = 3 cm and SD = 2 cm.

To Find:

1. The length of PD.
2. The perimeter of the quadrilateral PQRS.

Explanation:

We know that the length of tangents from an external point to a circle are equal.

According to the figure, this means that PA = PD, QB = QA, RC = RB and SD = SC.

Solution:

1. As we now know that PA = PD. So, the length of PD = PA = 5 cm.
2. Perimeter of the quadrilateral PQRS = The sum of all it's sides = Double the sum of those given sides = 2 ( 5 + 4 + 3 + 2 ) = 2 ( 14 ) = 28 cm

Answer:

1. The length of PD is 5cm.
2. Perimeter of the quadrilateral PQRS is 28 cm.

Answer 2

5 cm

area of quadrilateral =5+4+3+2×2=14×2=28