Please hurry .... Point Z is equidistant from the sides of RST which must be true?
2 answers:
Answer with explanation:
In Δ R ST, Z C ⊥ RT, Z B ⊥TS, and Z A ⊥ RS.
Draw a circle Passing through points A,B and C.
→→Z A=Z B=Z C=Radius of the circle having center Z.
The Angle between Radius and tangent line measures 90°.
Also, The theorem which we will use here to find out which option is true among four options is:
⇒Length of tangent from external point to a circle are equal.
In Δ ZAS and Δ ZBS
∠ ZAS = ∠ ZBS→→→Each being 90°
ZA=ZB→→→Radii of circle
SA=SB→→Length of tangent from external point to a circle are equal.
Δ ZAS ≅ Δ ZBS→→→→→[SAS]
∠ ASZ ≅ ∠BSZ→→→→→→[CPCT]
Option D: ∠ ASZ ≅ ∠BSZ is correct among four options.
You might be interested in
If we draw the diagonals of the octagonal gazebo, the 4 diagonals divide the octagon into 8 triangles.
Note that each triangle is an isosceles triangle whose equal sides are x, the radius of the circle.
The top angle of each triangle is obtained by dividing the full angle by 8.
So, each top angle =
= 45°
Now, in fig., consider one of the triangles Δ OAB. Draw an altitude OC from O to the opposite side AB.
This altitude OC bisects the top angle 45°.
Therefore, ∠ AOC = 22.5°.
Now, in Δ AOC,
So, AC = x sin 22.5°
Note that, AB = 2 AC.
Therefore, AB = 2x sin 22.5°.
Also,
So, OC = x cos 22.5°.
Area of Δ AOB =
= × (2x sin 22.5°) × (x cos 22.5°)
= (2 sin 22.5° cos 22.5°)
= sin 45°
= /
Area of the octagonal gazebo = 8 × one triangular area
= 8 × ( /
)
Area required for mulch = circular area - area of the gazebo
Now, cost per unit area = $1.50.
Hence, total cost g(m) = area × cost per unit area
Total cost g(m) = × 1.5
Hence, total cost g(m) = .
