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# geometry

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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.

Jan 22, 2022

#1
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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

Jan 23, 2022