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Circles Tangents Problems (view source)
Revision as of 05:33, 14 August 2014
, 05:33, 14 August 2014→Interpretation of problem
[[File:fig3.png|200px]]
[[File:fig3.png|200px]]
==Interpretation of problem==
==Interpretation of problem==
# In the quadrilateral ABCD sides BC , DC & QB are given .
#AD⊥DC.
# Asked to find the radius OS or OP
'''==Concepts used=='''
#Tangents drawn from an external point to a circle are equal.
#In a quadrilateral, if all angles are equal and a pair of adjacent sides are equal then it is a square
#In a circle, the radius drawn at the point of contact is perpendicular to the tangent
'''==Algorithm=='''
In the fig BC=38 cm and BQ=27 cm <br>
BQ=BR=27 cm (because by concept 1) <br>
Therefore, CR=BC-BR=38-27=11 cm <br>
CR=SC=11 cm (because by concept 1) <br>
DC=25 cm <br>
therefore , DS=DC-SC=25-11=14 cm <br>
DS=DP=14 cm (because by concept 1) <br>
Also {AD ortho DC} , {OP ortho AD} and {OS ortho DC} <br>
∠D=∠S=∠P=90˚ <br>
⇒ ∠O=90˚ <br>
therefore DSOP is a Square <br>
SO=OP=14 cm <br> hence Radius of given circle is 14 cm
=Problem 5=
=Problem 5=
A circle is touching the side BC of △ABC at P. AB and AC when produced are touching the circle at Q and R respectively. Prove that AQ =<math>\frac{1}{2}</math> [perimeter of △ABC].
A circle is touching the side BC of △ABC at P. AB and AC when produced are touching the circle at Q and R respectively. Prove that AQ =<math>\frac{1}{2}</math> [perimeter of △ABC].