CBSE Class 10 Answered
ABD is a right angled triangle at A and AC_|_BD show that
(I) AB²=BC.BD
(II) AC²=BC.DC
(III) AD²=BD.CD
Asked by mulkallaswapna | 15 Jan, 2020, 07:32: AM
Expert Answer
1.
ΔADB and ΔCAB
∠DAB = ∠ ACB (Each 90°)
∠ADB = ∠CBA (Common angle)
∴ ΔADB ∼ ΔCAB
AB/CB = BD/AB
AB² = BD*CB
∠DAB = ∠ ACB (Each 90°)
∠ADB = ∠CBA (Common angle)
∴ ΔADB ∼ ΔCAB
AB/CB = BD/AB
AB² = BD*CB
2.
ΔCBA
∠CAB = x
∠CBA = 180° - 90° - x
∠CBA = 90° - x
simillarly,
∠CAD = 90° - x
∠CDA = 180° - 90° - ( 90° - x )
∠CDA = x
In ΔCBA AND ΔCAD
∠CBA = ∠CAD
∠CAB = ∠CDA
∠ACB = ∠DCA
∴ ΔCBA ∼ ΔCAD
AC/DC = BC/AC
AC² = BC * DC
∠CAB = x
∠CBA = 180° - 90° - x
∠CBA = 90° - x
simillarly,
∠CAD = 90° - x
∠CDA = 180° - 90° - ( 90° - x )
∠CDA = x
In ΔCBA AND ΔCAD
∠CBA = ∠CAD
∠CAB = ∠CDA
∠ACB = ∠DCA
∴ ΔCBA ∼ ΔCAD
AC/DC = BC/AC
AC² = BC * DC
3.
ΔDCA and ΔDAB
∠DCA = ∠DAB
∠CDA = ∠ADB
∴ ΔDCA ∼ ΔDAB
DC/DA = DA/DB
AD² = CD * BD
∠DCA = ∠DAB
∠CDA = ∠ADB
∴ ΔDCA ∼ ΔDAB
DC/DA = DA/DB
AD² = CD * BD
Answered by Arun | 19 Jan, 2020, 05:06: PM
Application Videos
-
This video covers an application on distance and height
-
This video describe Relation between HCF and LCM. -
This video explains the concept of Arithmetic Progression, Solving Linear E... -
This video explains the concept of conversion of solids. -
This video explains how to find the volume of a frustum and a cone
Concept Videos
-
This video explains the statement of Euclid's Division lemma and algorithm ... -
Determination of H.C.F and L.C.M of numbers using Prime Factorization and ... -
Discuss rational and irrational numbers and express them on the number lin... -
Types, degree and zeroes of a polynomial. Find number of zeroes of the pol... -
Relationship between zeroes and coefficients of a polynomial. Formation of...
CBSE 10 - Maths
Asked by prasadshruti9999 | 03 Jun, 2023, 10:05: AM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by Akhandp457 | 29 May, 2023, 09:06: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by dimpaldihingia2 | 24 May, 2023, 06:10: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by akhilthainuan | 22 May, 2023, 02:11: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by ruchipandey20071978 | 21 May, 2023, 10:00: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by ruchipandey20071978 | 21 May, 2023, 09:57: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by ruchipandey20071978 | 21 May, 2023, 05:32: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by ruchipandey20071978 | 21 May, 2023, 05:29: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by ruchipandey20071978 | 11 May, 2023, 06:55: AM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by gavhanenisha0310 | 09 May, 2023, 04:10: PM
ANSWERED BY EXPERT