In a circle, prove that the tangents from an external point are equal. (NCERT Class 10, Circles – Important)

Answer: Let P be an external point, PA and PB tangents to circle with center O touching at A and B. OA ⟂ PA and OB ⟂ PB (radius ⟂ tangent). In right triangles △OAP and △OBP: OA=OB (radii), OP common, and both right-angled. By RHS congruence, △OAP ≅ △OBP ⇒ PA=PB. Hence tangents from an external point are equal.