Question

We are given points A, B,C and D in the plane such that AD = 13 while AB =BC=AC=CD=10 .

find angle angle ADB ..

Answer 1

Answer:

30 degrees

Step-by-step explanation:

ABCD is a quadrilateral where AC and BD are it's diagonals ABC is an equalater triangle and ACD is an iscosseles triangle angle,CAB equal to angle BCA equal to sixty degrees and if you equate this you will get answer

Answer 2

Consider the figure . There exist two possible locations for point D , so we instead denote them by D′ and D′′ .

C is the centre of a circle of radius 10 , and A the centre of a circle of radius 13 . Clearly , AC=AB=BC=CD′=CD′′=10 and AD′=AD′′=13

Since △ACB is equilateral , ∠ACB , the angle subtended at the centre of the circle , =60∘

∴∠AD′B and ∠AD′′B, the angles subtended at the circumference , equal half the angle subtended at the centre of the circle =12∠ACB=12⋅60∘=30∘