Question

Seg AB is a diameter of a circle with centre p. Segment AC is a chord .A secant Through p and parallel to seg AC intersects the tangent drawn at C in D prove that line DB is a tangent to the circle

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer with Step-by-step explanation:

In triangle ACP

PA=PC

Radius of circle are equal

Angle ACP=Angle CAP

Angle made by two equal sides are equal

AC is parallel to PD

Angle CAP=Angle DPB

Reason: Corresponding angles are equal

Angle ACP=Angle CPD

Reason:Alternate interior angle

Angle DPB=Angle CPD

In triangle DCP and DBP

PC=PB

Reason: all radius of circle are equal

PD=PD

Reason:Common segment

Angle DPB=Angle CPD

$\triangle$ DCP$\cong\triangle$DBP

Reason: SAS Postulate

Angle PCD=Angle PBD

Reason:CPCT

$\Angle PCD=90^{\circ}$, Radius is always perpendicular to tangent

Angle PCD=Angle PBD=$90^{\circ}$

Angle between PB and DB=90 degrees

Therefore, DB is  a tangent.

Hence, proved.

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