Question

In the following figure `O` is the centre of the circel. If `angleACB=60^(@)` and `DA=DB` then prove that `DeltaADB` is an equilateral triangle.

Answer 1

`angle ADB=angleACB` (angles of same segment)
`angle ADB=60^@`
`rArr`
In `Delta ADB`,
`AD=DB`
`AD=DB`
`rArrangle ABD=angle BAD`
and `angleABD+angleBAD +angle ADB=180^@`
`rArrangleABD+angle ABD+60^@=180^@`
`rArr2angle ABD=120^@`
` rArrangle ABD=60^@`
`thereforeangle ABD=angle BAD =angle ADB=60^@`
`rArrDelta ABD` is an equilateral triangle.