Question

In two concentric circles with centre O,PQ is the diameter of outer circle and QS is the tangent to the inner circle touching it in R and outer in S. find the length of PR, if radii of two circles are 13cm and 8cm

Answer 1

Answer:

PR = 19 cm

Step-by-step explanation:

From the figure,

i ) ∆PSR ~ ∆ORQ

$\frac{PS}{OR}=\frac{PQ}{PQ}$

$\implies \frac{PS}{8}=\frac{26}{13}$

$\implies PS = 2\times 8=16\:cm \:--(1)$

$ii) In \triangle ORQ,\\\angle ORQ =90\degree$

$QR^{2}=OQ^{2}-OR^{2}\\=13^{2}-8^{2}\\=169-64\\=105$

$\implies QR = \sqrt{105}\:--(2)$

$iii) \frac{QS}{QR}=\frac{PS}{OR}$

$\implies \frac{QS}{\sqrt{105}}=\frac{16}{8}$

$\implies QS = 2\sqrt{105}\:--(3)$

$SR = QS - QR\\=2\sqrt{105}-\sqrt{105}\\=\sqrt{105}\:---(4)$

$iv ) PR = \sqrt{PS^{2}+SR^{2}}$

$=\sqrt{16^{2}+105}\\=\sqrt{256+105}\\=\sqrt{361}\\=19\:cm$

Therefore,

PR = 19 cm

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Answer 2

Answer:

but the answer given is 5.26 cm