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In a park, four poles are standing at positions A, B, C and D around the circular fountain such that the cloth joining the poles AB, BC, CD and DA touches the circular fountain at P, Q, R and S respectively as shown in the figure.
Based on the above information, answer the following questions :
(i) If O is the centre of the circular fountain, then $\angle OSA = ...$
(ii) If AB = AD, then write the name of the figure ABCD.
(iii) (a) If DR = $7$ cm and AD = $11$ cm, then find the length of AP.
OR
(iii) (b) If O is the centre of the circular fountain with $\angle QCR = 60^\circ$, then find the measure of $\angle QOR$.
Based on the above information, answer the following questions :
(i) If O is the centre of the circular fountain, then $\angle OSA = ...$
(ii) If AB = AD, then write the name of the figure ABCD.
(iii) (a) If DR = $7$ cm and AD = $11$ cm, then find the length of AP.
OR
(iii) (b) If O is the centre of the circular fountain with $\angle QCR = 60^\circ$, then find the measure of $\angle QOR$.
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(i) $90^\circ$
(ii) $AB + DC = BC + DA$
Given, $AB = AD$
$\Rightarrow BC = DC$
So, ABCD is a Kite
(iii) (a) $DS = DR = 7$ cm
$AD = 11$ cm
$7+ SA = 11$
$\Rightarrow SA = 4$ cm
$\therefore AP = SA = 4$ cm
OR
(b) $\angle QOR = 180^\circ - 60^\circ$
$= 120^\circ$
(ii) $AB + DC = BC + DA$
Given, $AB = AD$
$\Rightarrow BC = DC$
So, ABCD is a Kite
(iii) (a) $DS = DR = 7$ cm
$AD = 11$ cm
$7+ SA = 11$
$\Rightarrow SA = 4$ cm
$\therefore AP = SA = 4$ cm
OR
(b) $\angle QOR = 180^\circ - 60^\circ$
$= 120^\circ$