Home
Class 12
MATHS
In A B C ,P is an interior point such t...

In ` A B C ,P` is an interior point such that `/_P A B=10^0/_P B A=20^0,/_P C A=30^0,/_P A C=40^0` then ` A B C` is isosoceles (b) right angled equilateral (d) obtuse angled

A

isosceles

B

right angled

C

equilateral

D

obtuse angled

Text Solution

Verified by Experts

The correct Answer is:
A

From `Delta APB, Delta PBC, and Delta PCA`, using sine rule
`(AP)/(sin angleABP) (BP)/(sin anglePCB) .(CP)/(sin angle PAC)`
`= (AP)/(sin anglePCA) .(CP)/(sin anglePBC).(BP)/(sin anglePAB)`
`rArr sin30^(@) .sinx .sin 10^(@) = 2in 20^(@) .sin (80^(@) -x) sin 40^(@)`
`rArr x = 60^(@)`
`:. angle BCA = angle CAB = 50^(@)`
So, `DeltaABC` is an isosceles triangle
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Multiple correct answer type|24 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Linked comprehension type|34 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Concept application exercise 5.11|4 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE )|8 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1119 Videos

Similar Questions

Explore conceptually related problems

In A B C ,P is an interior point such that /_P A B=10^0/_P B A=20^0,/_P C A=30^0,/_P A C=40^0 then A B C is (a) isosoceles (b) right angled (c) obtuse angled

If two events A and B such that P(A')=0.3 , P(B)=0.5 and P(AnnB)=0.3 , then P(AnnB') is

If A and B are two events such that P(A)=0.3 , P(B)=0.25 , P(AnnB)=0.2 , then P(((A^(C ))/(B^(C )))^(C )) is equal to

If in A B C , side a , b , c are in A.P. then B > 60^0 (b) B<60^0 Blt=60^0 (d) B=|A-C|

A and B are two independent events such that P(A^C) = 0.7, P(B) = k and P(A uB) = 0.8 , then K is

If A and B are two events then show that P(B) = P(A). P(B/A) + P(A^C).P(B/A^C).0 < P(A) < 1 .

In triangle A B C ,/_A=60^0,/_B=40^0,a n d/_C=80^0dot If P is the center of the circumcircle of triangle A B C with radius unity, then the radius of the circumcircle of triangle B P C is (a) 1 (b) sqrt(3) (c) 2 (d) sqrt(3) 2

The chord P Q of the rectangular hyperbola x y=a^2 meets the axis of x at A ; C is the midpoint of P Q ; and O is the origin. Then A C O is (a) equilateral (b) isosceles (c) right-angled (d) right isosceles

If P(A) = 0.2, P(B) = 0.4, P(AB) = 0.08, then P(B/A^c) equals to

If A and B are two events associated with a random experiment such that P(B) = 0.35, P(A or B) = 0.85 and P(A and B) = 0.15, find P(A).

CENGAGE PUBLICATION-PROPERTIES AND SOLUTIONS OF TRIANGLE-Exercises
  1. If D is the mid-point of the side B C of triangle A B C and A D is per...

    Text Solution

    |

  2. In a triangle ABC, if cotA :cotB :cotC = 30: 19 : 6 then the sides a, ...

    Text Solution

    |

  3. In A B C ,P is an interior point such that /P A B=10^0/P B A=20^0,/P ...

    Text Solution

    |

  4. In A B C , if A B=c is fixed, and cosA+cosB+2cos C=2 then the locus o...

    Text Solution

    |

  5. If in A B C ,A=pi/7,B=(2pi)/7,C=(4pi)/7 then a^2+b^2+c^2 must be (a)R...

    Text Solution

    |

  6. In Delta ABC, "cot"(A)/(2) + "cot" (B)/(2) + "cot" (C)/(2) is equal to

    Text Solution

    |

  7. In A B C ,(cot (A/2)+cot(B/2))(asin^2(B/2)+bsin^2(A/2))= (a) cotC (...

    Text Solution

    |

  8. In a right-angled isosceles triangle, the ratio of the circumradius an...

    Text Solution

    |

  9. In a ΔABC, a semicircle is inscribed, whose diameter lies on the side ...

    Text Solution

    |

  10. In A B C ,A(2pi)/3,b-c=3sqrt(3)c m and area of A B C=(9sqrt(3))/2c m...

    Text Solution

    |

  11. In triangle A B C , let /c=pi/2dot If r is the inradius and R is circu...

    Text Solution

    |

  12. In the given figure A B is the diameter of the circle, centred at Odot...

    Text Solution

    |

  13. In triangle A B C ,ifPdotQ ,R divides sidesB C ,A C , and A B , respec...

    Text Solution

    |

  14. If the angles of a triangle are 30^0a n d45^0 and the included side is...

    Text Solution

    |

  15. In triangle A B C , base B C and area of triangle are fixed. The locus...

    Text Solution

    |

  16. Let the area of triangle ABC be (sqrt3 -1)//2, b = 2 and c = (sqrt3 -1...

    Text Solution

    |

  17. In triangleABC ,Delta=6, abc=60, r=1 Then the value of 1/a+1/b+1/c is ...

    Text Solution

    |

  18. Triangle ABC is isosceles with AB=AC and BC=65cm. P is a point on BC s...

    Text Solution

    |

  19. In an equilateral triangle, the inradius, circumradius, and one of the...

    Text Solution

    |

  20. In triangle A B C , if cosA+cosB+cosC=7/4, t h e n R/r is equal to 3/4...

    Text Solution

    |