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.
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let me know if the propositions they gave don't match with mine.
thanks
Those two angles are complementary - which means they both give us 90 degrees. We know that all three angles in any triangle must be exactly 180 degrees, so the third angle will be 180 - 90 = 90 degrees. It means that our triangle is a <u>straight triangle</u>. The figure will look more less like in the attachment.
