PR is tangent to a circle at point P. Q is another point on circle such that PQ is diameter of circle and RQ cuts circle at M. if radius of circle is 4 units and PR=6units. find ratio of triangle PMR to PQR. optn
a)11/20
b)3/5
c)13/20
d)18/25

• PR^2+PQ^2=QR^2
  8^2+6^2=QR^2
  QR=10
  
  NOW TO FIND THE RATIO OF PERIMETER OF TWO TRIANGLE TAKE THE OF UNCOMMON ANGLE i.e,
  angle QPR
  
  so COS (QPR)= COS (PR/QR)
  =6/10
  =3/5 (ANSWER)
• 9 years agoHelpfull: Yes(12) No(3)
• let PM = y
  QM= x
  MR = 10-x
  In triangle PQM,
  PM^2+QM^2 = PQ^2
  => x^2+y^2=64 .....(1)
  In triangle PMR,
  PM^2+ MR^2= PR^2
  y^2+(10-x)^2=36......(2)
  solving for x and y
  x=6.4
  y=4.8
  taking permineter of triangle PQR =24
  perimeter of triangle PMR = 14.4
  take ratio 14.4/24= 0.6
  so option (c) is right..
• 9 years agoHelpfull: Yes(10) No(5)
• PQ^2+PR^2=QR^2
  QR=10
  
  PM^2+RM^2=6^2(PR=6)
  PM^2+QM^2(which is (10-RM)^2)=8^2(pq=8)
  using above to equations we found rm=3.6 (so qm=10-3.6=4.8)and pm=4.8
  now finding perimeter of both triangles we get ratio as 3/5
• 9 years agoHelpfull: Yes(6) No(2)
• Given PQ = 8 cm (Diameter of Circle)
  PR = 6 cm (Tangent to the circle)
  Therefore QR = 10cm
  Let QM = x and PM = y ; MR = 10-x
  PM^2 + MQ^2 = PQ^2 or x^2 + y^2 = 64 ........ (i)
  
  MR^2 + PM^2 = PR^2
  
  or (10 - x)^2 + y^2 = 36 ...... (ii)
  Subtracting (ii) from (i)
  
  
  (x + 10 - x )(x - 10 +x) = 28
  
  10(2x -10) = 28
  
  x = 6.4
  By solving we get y=4.8
  (perimeter of PMR)/(perimeter of PQR)=(4.8+3.6+6)/(8+10+6)=14.4/24=3/5
  answer option (b)3/5
• 9 years agoHelpfull: Yes(6) No(0)
• U ll get QR=10 , PMR and PQR r two right ang. triangles
  
  (PR common side, PRQ common angle , two right angles RPQ and PMR ) So they are similar.
  
  now as per the similarity rule (ratio of sides = ratio of triangles)
  i.e U can take PR/RQ=RPM/PQR = 6/10, or find MR and compare u ll get same ans.
  
• 9 years agoHelpfull: Yes(5) No(0)
• " RQ cuts circle at M"..@rohit ,justify this first in your answer.then i ll hit a like on it :)
• 9 years agoHelpfull: Yes(4) No(5)
• perimeter
  
• 9 years agoHelpfull: Yes(2) No(0)
• Ans. 3/5
  Given PQ = 8 cm (Diameter of Circle)
  PR = 6 cm (Tangent to the circle)
  Therefore QR = 10cm
  Let QM = x and PM = y ; MR = 10-x
  PM^2 + MQ^2 = PQ^2 or x^2 + y^2 = 64 ........ (i)
  
  MR^2 + PM^2 = PR^2
  
  or (10 - x)^2 + y^2 = 36 ...... (ii)
  Subtracting (ii) from (i)
  
  
  (x + 10 - x )(x - 10 +x) = 28
  
  10(2x -10) = 28
  
  x = 6.4
  By solving we get
  
  
• 9 years agoHelpfull: Yes(1) No(0)
• Anjali can you please shut your mouth
• 7 years agoHelpfull: Yes(1) No(2)
• @Jignesh ,can u talk politely to Anjali!such a barbarian u r.learn manners
• 7 years agoHelpfull: Yes(1) No(1)
• Since PR is tangent, angle RPQ = 90°. Hence QPR is a right angled triangle.
  
  Given that PR = 6 units ----(1)
  PQ = Diameter of the circle = 2×4 = 8 units ----(2)
  
  Using Pythagorean theorem, QR2 = PR2 + PQ2 = 62+82 = 100
  => QR = 10 units ----(3)
  
  Angle inscribed in a semicircle is always 90° (Thales' theorem)
  => angle PMQ is 90°
  
  sin PRM = sin PRQ
  PM/PR=PQ/RQ
  PM/6=8/10
  => PM = 48/10 = 4.8 units ----(3)
  
  tan PRM = tan PRQ
  PM/RM=PQ/PR
  4.8/RM=86
  => RM = 3.6 units ----(4)
  
  Perimeter of triangle PMR = PM + RM + PR = 4.8 + 3.6 + 6 = 14.4 units
  Perimeter of triangle PQR = PQ + QR + PR = 8 + 10 + 6 = 24 units
  
  Perimeter of triangle PMR/Perimeter of triangle PQR=14.4/24=144/240= 3/5
• 7 years agoHelpfull: Yes(1) No(0)
• ratio of triangle....i mean ratio of what..their areas or their perimeters
• 9 years agoHelpfull: Yes(0) No(0)
• isn't the answer comes 13/20 guys!!!!
• 9 years agoHelpfull: Yes(0) No(14)
• anjali can u post ur solution
• 9 years agoHelpfull: Yes(0) No(0)
• rohit ....how ratio of perimeter is equal to cosin of angle ??? please explain...
• 9 years agoHelpfull: Yes(0) No(0)