Prove that the length of two tangents drawn from an external point to a circle r equal
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Answer is on Page-211 Of CBSE NCERT MATHEMATICS TEXTBOOK.It is Theorem 10.2.
GIVEN:Let there be a circle with centre O,a point P lying outside the circle with two tangents PQ,PR on the circle from P.
TO PROVE:PQ=PR
PROOF:
Join OP,OQ and OR.
angle OQP AND ORP ARE right tangles because these are between radii and tangents,and according to theorem that tangent at any point of cicle is perpendicular to the radius through the point of contact;they are right angles.
In Triangles OQP and ORP,
OQ=OR(Radii of same circle)
OP=OP(Common)
Triangle OQP IS CONGRUENT TO Triangle ORP BY RHS CONGRUENCY.
THEREFORE,PQ=PR
Hope this helps.Please Mark my answer as BRAINLIEST...!!!
GIVEN:Let there be a circle with centre O,a point P lying outside the circle with two tangents PQ,PR on the circle from P.
TO PROVE:PQ=PR
PROOF:
Join OP,OQ and OR.
angle OQP AND ORP ARE right tangles because these are between radii and tangents,and according to theorem that tangent at any point of cicle is perpendicular to the radius through the point of contact;they are right angles.
In Triangles OQP and ORP,
OQ=OR(Radii of same circle)
OP=OP(Common)
Triangle OQP IS CONGRUENT TO Triangle ORP BY RHS CONGRUENCY.
THEREFORE,PQ=PR
Hope this helps.Please Mark my answer as BRAINLIEST...!!!
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