Question

prove that the tangents to acircle at the end point of a diameter are parallel​

Answer 1

Answer:

Let AB be a diameter of the circle. Two tangents PQ and RS are drawn at points A and B respectively. Radius drawn to these tangents will be perpendicular to the tangents. Since alternate interior angles are equal, lines PQ and RS will be parallel

Answer 2

Step-by-step explanation:

we have a circle with centre O PA and PB are two tangents on circle,

join O to A and O to B and P to O,

NOW we have two triangles PBO and PAO,

by theorem 10.1 we know tangent to a circle is perpendicular to radius at point of contact,

so. angle OAP and OBP is 90,

now in triangle PBO and PAO,

OAP=OBP(90 EACH)

PO=PO(COMMON)

OPB=OPA(SAME RADII),

by RHS TRIANGLES ARE CONGRUENT, BY

CPCT PA=PB

THEREFORE PA II PB (CPCT),

HP