Home
Class 12
MATHS
In a triangle ABC with angleA=90^(@), P ...

In a triangle ABC with `angleA=90^(@)`, P is a point on BC such that PA : PB = 3 : 4 If `AB=sqrt7" and " AC=sqrt5` then BP : PC is-

A

`2:1`

B

`:3`

C

`4:5`

D

`8:7`

Text Solution

Verified by Experts

The correct Answer is:
A

`tantheta=(sqrt5)/(sqrt7),sin theta=(sqrt5)/(sqrt12),cos theta=(sqrt7)/(sqrt12)`
In `DeltaAPB` using sine rule
`(3X)/(sin theta)=(4X)/(sin alpha)=(sqrt7)/(sin(180^(@)-(theta+alpha)))`
`sin alpha=4/3sin theta=4/3xxsqrt5/sqrt12=(2sqrt5)/(3sqrt5)=sqrt20/sqrt27`
`rArrcosalpha=sqrt7/sqrt27`
`&3xsin(theta+alpha)=sqrt7sin theta`
`rArr 3x(cosalpha+cotthetasinalpha)=sqrt7`
`rArr3x((sqrt3)/sqrt27)+sqrt7/sqrt5sqrt20/sqrt27)=sqrt7`
`3x xx1/sqrt3=1`
`x=1/sqrt3`
`:. (BP)/(PC)=(4x)/(sqrt(12)-4x)=1/((2sqrt3)/(4//sqrt3)-1)=4/(6-4)=2/1`
Promotional Banner

Topper's Solved these Questions

  • KVPY

    KVPY PREVIOUS YEAR|Exercise Matematics|20 Videos

  • KVPY

    KVPY PREVIOUS YEAR|Exercise Part 1 Mathematics|45 Videos

  • KVPY

    KVPY PREVIOUS YEAR|Exercise PART-2 MATHMATICS|10 Videos

  • KVPY 2021

    KVPY PREVIOUS YEAR|Exercise PART II MATHEMATICS|4 Videos

Similar Questions

Explore conceptually related problems

In right triangle ABC , AB=BC , then angleA is equal to

In any triangle ABC, if angle C=90^@ , AC=4 unit, BC=3, find AB.

In triangle ABC ,P is a point on BC such that BP : PC = 3 : 4 and Q is the midpoint of BP. Then ar(triangle ABQ) :ar (triangle ABC) is equal to: त्रिभुज ABC में, P, BC पर स्थित एक ऐसा बिंदु है कि BP : PC = 3 : 4 है और Q, BP का मध्य बिंदु है | ar(triangle ABQ) : ar(triangle ABC) का मान ज्ञात करें |

In triangle ABC ,P is a point on BC such that BP : PC = 2 : 3 and Q is the midpoint of BP. Then (triangle ABQ) : (triangle ABC) is equal to: त्रिभुज ABC में, P, BC पर स्थित एक ऐसा बिंदु है कि BP : PC = 2 : 3 है और Q, BP का मध्य बिंदु है | (triangle ABQ) : (triangle ABC) ज्ञात करें |

In triangle ABC ,P is a point on BC such that BP : PC = 4:5 and Q is the midpoint of BP. Then ar(triangle ABQ) : ar(triangle ABC) is equal to: त्रिभुज ABC में, P, BC पर स्थित एक ऐसा बिंदु है कि BP : PC = 4:5 है और Q, BP का मध्य बिंदु है | ar(triangle ABQ) : ar(triangle ABC) का मान ज्ञात करें |

In DeltaABC,angleB=90^(@). If P is the mid-point of side AC, then PA=PB=

In triangle ABC ,P is a point on BC such that BP : PC = 4 : 11 and Q is the midpoint of BP. Then ar(triangle ABQ) :ar (triangle ABC) is equal to: त्रिभुज ABC में, P, BC पर स्थित एक ऐसा बिंदु है कि BP : PC = 4 : 11 है और Q, BP का मध्य बिंदु है | ar(triangle ABQ) : ar(triangle ABC) का मान किसके बराबर होगा ?

In triangle ABC ,P is a point on BC such that BP : PC = 4 : 3 and Q is the midpoint of BP. Then ar(triangle ABQ) :ar (triangle ACB) is equal to: त्रिभुज ABC में, P, BC पर स्थित एक ऐसा बिंदु है कि BP : PC = 4 : 3 है और Q, BP का मध्य बिंदु है | ar(triangle ABQ) : ar(triangle ACB) का मान ज्ञात करें |

In triangle ABC ,P is a point on BC such that BP : PC = 1 : 2 and Q is the mid point of BP. then, ar(triangle ABQ) :ar (triangle ABC) is equal to: त्रिभुज ABC में, P, BC पर स्थित ऐसा बिंदु है कि BP : PC = 1 : 2 है और Q, BP का मध्य बिंदु है | तो ar(triangle ABQ) :ar (triangle ABC) का मान क्या होगा ?