The photos come after Prince William and Kate shared new photos of their family to celebrate Father's Day, showing the duke with his three children, Prince Louis, 3; Prince Charlotte, 6; and Prince George, seven.
For the day, Prince William spent it with his two eldest kids as they assisted him with the half marathon events which were held at the Queen's Sandringham Estate.
Prince William, Prince George and Princess Charlotte were seen at the beginning of the event in Sandringham, Norfolk.
The three of them were spotted waving at the competitors enthusiastically as they passed them by.
Prince William appeared smiling and relaxed today, despite reports he "threw Prince Harry out" of their joint household at Kensington Palace following a blistering row between the brothers. The clash has been detailed by historian and biographer Robert Lacey, in his book Battle of Brothers which is being serialised in The Times.
Prince William's good spirits come after his ongoing conflicts with brother Prince Harry, who William is concerned will soon go "too far" with his public truth bombs.
The Duke of Cambridge is said to be worried his younger brother could further damage his relationships with the royal family.
And a friend told the Mail on Sunday William is both disappointed and "greatly concerned" by Harry's latest broadside in yet another Oprah production.
Prince Charles came in for particular criticism in Harry's latest documentary, The Me You Can't See.
In the programme, Harry accused the royals of showing "total neglect" for his mental health woes.
And he claimed Charles caused him to "suffer" and didn't "make it right" for him after his mother's death in 1997.
He also spoke about Meghan's battles with mental health – and said she would sob into her pillow after "smears" from The Firm.
