In an isosceles △ABC (AC = BC) its incircle touches the side BC at point T. Given AC = 4 and AT = 3. Find the length of AB.

Guest Jan 22, 2022

#1**-5 **

Isosceles triangle ABC has AC = BC = 4.

Using the rules of tangents, AT is perpendicular to a leg of triangle ABC. AC = 4 and AT = 3, so using the pythagorean theorem we can get length of segment CT.

CT = \(\sqrt{4^2 - 3^2}\) = \(\sqrt{7}\)

Segment BT = BC - TC = \(4 - \sqrt{7}\)

Then we can use the pythagorean theorem to get AB.

AB = \(\sqrt{3^2 + (4 - \sqrt{7})^2}\)

AB = \(2\sqrt{8 - 2\sqrt{7}}\)

pro maths

proyaop Jan 23, 2022