In the rhombus abcd, angle dba is 60 if de is 8.5cm

Check the picture below.

in a rhombus, the diagonals meet always at right angles, namely the angles at vertex E are all 90°.

also, the diagonals cut each other at equal halves, namely DE = EB, and since we know DE = 8.5, then EB = 8.5..

we also know ∡DBA is 60°, that makes all triangles a 30-60-90 triangle, including the triangle ABE, and using the 30-60-90 rule as you see in the picture, then we get that much.

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12