Request a call back

In the figure, OP is equal to the diameter of the circle. Prove that ABP is an equilateral triangle.
Asked by Topperlearning User | 27 Jul, 2017, 01:09: PM

OP = 2r………given,OP= diameter of the circle

OAP = 90o (Tangent is to the radius through the point of contact)

In right OAP

sin (OPA) =

OPA = 30o

Similarly OPB = 30o

APB = 30o + 30o = 60o

Since PA = PB (Lengths of tangents from an external point are equal)

PAB = PBA

In APB,

APB + PAB + PBA = 180o (angle sum property)

60o + 2PAB = 180o

PAB = 60o

PBA = 60o

Since all angles are 60o, ABP is equilateral triangle.

Answered by | 27 Jul, 2017, 03:09: PM

## Application Videos

CBSE 10 - Maths
Asked by riazu945 | 16 Jan, 2022, 01:00: PM
CBSE 10 - Maths
Asked by sangyaswarupa | 16 Mar, 2021, 10:06: AM
CBSE 10 - Maths
Asked by sinhkaran79 | 14 Mar, 2021, 12:59: PM
CBSE 10 - Maths
Asked by s.saumya1011 | 05 Nov, 2020, 02:10: PM
CBSE 10 - Maths
Asked by brjkishorchauhan03 | 04 Nov, 2020, 12:10: PM
CBSE 10 - Maths
Asked by arindeep.singh | 02 Oct, 2020, 01:20: PM