Question

Two circles whose centres are A and B touches each other at point P. A line CD is drawn which passing through point P, which meets its circumference at C and D. Then prove that:AC is parallel to BD​

Answer 1

Given : Two circles whose centres are A and B touches each other at point P. A line CD is drawn which passing through point P, which meets its circumference at C and D.

To Find : Prove that AC is parallel to BD

Solution:

∠APC = ∠BPD  ( Vertically opposite angles)

in ΔAPC

AP = AC = Radius

=> ∠ACP = ∠APC

in ΔBPD

BP = BD = Radius

=> ∠BDP = ∠BPD

∠ACP = ∠APC

∠BDP = ∠BPD

∠APC = ∠BPD

=>  ∠ACP =  ∠BDP

=> AC || BD   as alternate angles  are equal ( CD is transversal )

QED

Hence Proved

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