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In the Given Figure, Ab is the Diameter of the Circle, with Centre O, and at is the Tangent. Calculate the Numerical Value of X. - ICSE Class 10 - Mathematics

ConceptTangent Properties - If a Line Touches a Circle and from the Point of Contact, a Chord is Drawn, the Angles Between the Tangent and the Chord Are Respectively Equal to the Angles in the Corresponding Alternate Segments

Question

In the given figure, AB is the diameter of the circle, with centre O, and AT is the tangent. Calculate the numerical value of x.

Solution

In Δ OBC ,

OB = OC  (Radii of the same circle)

∴ ∠ OBC = ∠ OCB

But ,Ext ∠ COA = ∠ OBC + ∠OCB

Ext . ∠COA = 2 ∠ OBC

⇒ 64° = 2∠OBC

⇒ ∠ OBC = 32°

Now in Δ ABT

∠BAT = 90° (OA ⊥ AT )

∠ OBC or ∠ ABT = 32°

∴ ∠ BAT + ∠ ABT + X° = 180°

⇒ 90°  + 32 °  + X°  =180°

⇒ X° = 58°

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Solution In the Given Figure, Ab is the Diameter of the Circle, with Centre O, and at is the Tangent. Calculate the Numerical Value of X. Concept: Tangent Properties - If a Line Touches a Circle and from the Point of Contact, a Chord is Drawn, the Angles Between the Tangent and the Chord Are Respectively Equal to the Angles in the Corresponding Alternate Segments.
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