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In XY and XY are two …

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In XY and XY are two parallel tangent to circle with centre O and another tangent AB with point pf contact C intresecting XY at A and XY at B. Prove that angle AOB =90 degree.

Posted by Sanjukta Buragohain 3 years, 9 months ago

CBSE > Class 10 > Mathematics

1 answers

Shwêtã Árîc 3 years, 9 months ago

Let us join point O to C In ΔOPAandΔOCA OP=OC (Radii of the same circle) AP=AC (Tangent from point A) AO=AO (Common side) ΔOPA≅ΔOCA (SSS congruence criterion) Therefore, P=C,A=A,O=O ∠POA=∠COA.........(1) Similarly, ∠QOB≅∠OCB ∠QOB=∠COB.........(2) Since,POQ is a diameter of the circle, it is a straight line. Therefore, ∠POA+∠COA+∠COB+∠QOB=180∘ So, from equation (1) and equation (2) 2∠COA+2∠COB=180∘∠COA+∠COB=90∘∠AOB=90∘

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