#### Question

The following figure shows a circle with PR as its diameter.

If PQ = 7 cm and QR = 3RS = 6 cm, find the perimeter of the cyclic quadrilateral PQRS.

#### Solution

In the figure, PQRS is a cyclic quadrilateral in which PR is a diameter

PQ = 7 cm

QR = 3 RS = 6 cm

3 RS = 6 cm ⇒ RS = 2 cm

Now in ∆PQR,

∠Q = 90° [Angles in a semi circle]

`PR^ 2 = PQ^2 + QR^2` [Pythagoras theorem]

= `72^2 + 62^2`

= 49 + 36

= 85

Again in right= `ΔPSQ, PR^2 =PS^2 + RS^2`

`85 = PS^2 + 2^2`

`PS^2 = 85 - 4 = 81 = (9)^2`

PS = 9cm

Now, perimeter of quad PQRS = PQ + QR + RS + SP

= (7 + 9 + 6 )cm

= 24

Is there an error in this question or solution?

Solution The Following Figure Shows a Circle with Pr as Its Diameter. If Pq = 7 Cm and Qr = 3rs = 6 Cm, Find the Perimeter of the Cyclic Quadrilateral Pqrs. Concept: Arc and Chord Properties - Angle in a Semi-circle is a Right Angle.