CBSE Class 10 Answered
Prove
that the lengths of tangents drawn from an external point to a circle are
equal.
Asked by Topperlearning User | 27 Jul, 2017, 01:09: PM
Expert Answer
Given: A circle with centre O; PA and PB are two tangents to the circle drawn from an external point P.
To prove: PA = PB
Construction: Join OA, OB, and OP.
It is known that a tangent at any point of a circle is perpendicular to the radius through the point of contact.
OA PA and OB PB
OAP = OBP = 90o ... (1)
In OPA and OPB,
OAP = OBP (Using (1))
OA = OB (Radii of the same circle)
OP = PO (Common side)
Therefore, OPA OPB (RHS congruency criterion)
PA = PB (Corresponding parts of congruent triangles are equal)
Thus, it is proved that the lengths of the two tangents drawn from an external point to a circle are equal.
Answered by | 27 Jul, 2017, 03:09: PM
Application Videos
Concept Videos
CBSE 10 - Maths
Asked by riazu945 | 16 Jan, 2022, 01:00: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by sinhkaran79 | 14 Mar, 2021, 12:59: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by s.saumya1011 | 05 Nov, 2020, 02:10: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by brjkishorchauhan03 | 04 Nov, 2020, 12:10: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by shivappahb308 | 21 Sep, 2020, 02:15: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by VasupradUboveja376 | 22 Jun, 2020, 12:03: AM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by njha25901 | 19 May, 2020, 07:20: AM
ANSWERED BY EXPERT