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ICSE Class 10 Answered

  the attitudes CM and BN of triangle ABC meet at H Prove that- 1-fraction numerator H C over denominator HB end fraction equals square root of fraction numerator CN times HN over denominator BM times HM end fraction end root 2-  triangle MHN is similar to two Triangle BHC.
Asked by shreyanshsri2004 | 20 May, 2019, 12:57: PM
answered-by-expert Expert Answer
S i n c e space C M space a n d space B N space a r e space a l t i t u d e s space o f space t r i a n g l e space A B C space a n d space t h e y space m e e t space a t space H
rightwards double arrow H space i s space t h e space o r t h o c e n t r e space o f space A B C
rightwards double arrow fraction numerator C H over denominator H M end fraction equals fraction numerator B H over denominator H N end fraction
I n space t r i a n g l e s space C H N space a n d space B H M
angle C H N equals angle B H M space..... space A l t e r n a t e space o p p o s i t e space a n g l e s
angle C N H equals angle B M H space.... space E a c h space 90 degree
A l s o comma space fraction numerator C H over denominator H M end fraction equals fraction numerator B H over denominator H N end fraction
T h e r e f o r e comma space triangle C H N almost equal to triangle B H M
U sin g space C. P. C. T
rightwards double arrow fraction numerator H C over denominator H B end fraction equals fraction numerator C N over denominator B M end fraction space a n d space fraction numerator H C over denominator H B end fraction equals fraction numerator H N over denominator H M end fraction
M u l t i p l y i n g space b o t h space t h e space e q u a t i o n s space w e space g e t
fraction numerator H C squared over denominator H B squared end fraction equals fraction numerator C N times H N over denominator B M times H M end fraction
rightwards double arrow fraction numerator H C over denominator H B end fraction equals square root of fraction numerator C N times H N over denominator B M times H M end fraction end root
I n space triangle M H N space a n d space triangle B H C comma
fraction numerator H C over denominator H B end fraction equals fraction numerator H N over denominator H M end fraction
a n d space angle B H C equals angle M H N space.... space A l t e r n a t e space o p p o s i t e space a n g l e s
rightwards double arrow triangle B H C almost equal to triangle M H N
Answered by Renu Varma | 20 May, 2019, 05:56: PM
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