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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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#### Video TutorialsVIEW ALL [1]

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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