ICSE Class 10CISCE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

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. - ICSE Class 10 - Mathematics

Login
Create free account


      Forgot password?

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?

Video TutorialsVIEW ALL [1]

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.
S
View in app×