9.0.69hord of a circle with centre O, AOC is a diameter and AT is the

1.	9.0.69hord of a circle with centre O, AOC is a diameter and AT is the tangent at Aa1 AB is awn in Fig. 8.70. Prove that <BAT = <ACB.asINCERT EXEMPLAR]
Answer» Let ∠ACB = x and ∠BAT = y.A tangent makes an angle of 90 degrees with the radius of a circle,so we know that ∠OAB + y = 900……..(1)The angle in a semi-circle is 90, so ∠CBA = 900. ∠CBA + ∠OAB + ∠ACB = 1800 (Angle sum property of a triangle) Therefore, 90 + ∠OAB + x = 1800So, ∠OAB + x = 900………….(2)But OAB + y = 900, Therefore, ∠OAB + y = ∠OAB + x ………….[From (1) and (2)]x = y.Hence ∠ACB = ∠BAT.

9.0.69hord of a circle with centre O, AOC is a diameter and AT is the tangent at Aa1 AB is awn in Fig. 8.70. Prove that <BAT = <ACB.asINCERT EXEMPLAR]

Answer»

Let ∠ACB = x and ∠BAT = y.A tangent makes an angle of 90 degrees with the radius of a circle,so we know that ∠OAB + y = 900……..(1)The angle in a semi-circle is 90, so ∠CBA = 900.

∠CBA + ∠OAB + ∠ACB = 1800 (Angle sum property of a triangle)

Therefore, 90 + ∠OAB + x = 1800So, ∠OAB + x = 900………….(2)But OAB + y = 900, Therefore, ∠OAB + y = ∠OAB + x ………….[From (1) and (2)]x = y.Hence ∠ACB = ∠BAT.

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9.0.69hord of a circle with centre O, AOC is a diameter and AT is the tangent at Aa1 AB is awn in Fig. 8.70. Prove that &lt;BAT = &lt;ACB.asINCERT EXEMPLAR]

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9.0.69hord of a circle with centre O, AOC is a diameter and AT is the tangent at Aa1 AB is awn in Fig. 8.70. Prove that <BAT = <ACB.asINCERT EXEMPLAR]