PQ is a common tangent of two circles that touches the two circles at point A and B respectively . prove that extended AB bisects PQ.?
Answers
Let PQ be the common tangent through P, where Q is the point that meets AB
Now, QA=QP (Tangents to the circle from the same point)
QP=QB (Tangents to the circle from the same point)
Thus, QA=QP=QB
Thus, Points A,B,P lie on the circle with centre Q and AB as the diameter.
Thus, ∠APB=90
∘
(Angle in a semi-circle)
Answer:
Let PQ be the common tangent through P, where Q is the point that meets AB
Now, QA=QP (Tangents to the circle from the same point)
QP=QB (Tangents to the circle from the same point)
Thus, QA=QP=QB
Thus, Points A,B,P lie on the circle with centre Q and AB as the diameter.
Thus, ∠APB=90
∘
(Angle in a semi-circle)
Step-by-step explanation:
Let PQ be the common tangent through P, where Q is the point that meets AB
Now, QA=QP (Tangents to the circle from the same point)
QP=QB (Tangents to the circle from the same point)
Thus, QA=QP=QB
Thus, Points A,B,P lie on the circle with centre Q and AB as the diameter.
Thus, ∠APB=90
∘
(Angle in a semi-circle)