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The Given Figure Shows a Circle with Centre O and Bcd is Tangent to It at C. Show That: ∠Acd + ∠Bac = 90° - Mathematics

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Question

The given figure shows a circle with centre O and BCD is tangent to it at C. Show that: ∠ACD + ∠BAC = 90°

Solution

Join OC.
BCD is the tangent and OC is the radius.

∴ OC ⊥ BD 

⇒ `∠`OCD = 90°

⇒ `∠`OCA + `∠`ACD = 90°

But in ΔOCA
OA = OC (radii of same circle)

∴ `∠` OAC + `∠` OAC 

Substituting (i)

`∠` OAC + `∠`ACD = 90°

⇒ `∠`BAC + `∠`ACD = 90°

 

 

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APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 18: Tangents and Intersecting Chords
Exercise 18 (C) | Q: 16 | Page no. 285
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The Given Figure Shows a Circle with Centre O and Bcd is Tangent to It at C. Show That: ∠Acd + ∠Bac = 90° Concept: Tangent to a Circle.
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