The length of the larger diagonal of the rhombus is 68, the radius of the circle inscribed in the rhombus is 8.

| February 22, 2021 | education

The length of the larger diagonal of the rhombus is 68, the radius of the circle inscribed in the rhombus is 8. Find the distance from the top of the acute angle of the rhombus to the nearest point of contact of the circle inscribed in the rhombus with the side of this rhombus.

First, let’s draw a rhombus, marking the vertices as ABCP.

Then we will inscribe a circle in it, designating the points of tangency to the sides AB and AP as K and T.

The center of circle O lies at the intersection of the diagonals.

Since the diagonal AC at point O is divided in half, then AO = 68/2 = 34 cm.

Consider a triangle AOT, in it OT is the radius, and AT is the distance from the top of the acute angle of the rhombus to the nearest point of contact, therefore AT = √ (34 ^ 2 – 8 ^ 2) = 2√273 cm.



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