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37. Let M be ...

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37. Let M be a point of contact of two internally touching circles . Let line AMB be their common tangent . The chord CD of the bigger circle touches the smaller circle at point N and chord CM and chord DM of bigger circle intersect the smaller circle at points P&R respectively . Prove that ANGLE CMN = ANGLE DMN

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Q. Let M be a point of contact of two internally touching circles. Let line AMB be their common tangent.The chord CD of the bigger circle touches the smaller circle at point N and chord DM of the bigger circle touches the smaller circle at the points P and R respectively.

∠ CMN ≅ ∠ DMN

Q. Prove that "In two concentric circles, a chord of the bigger circle, that touches the smaller circle is bisected at the point of contact with the smaller circle."

Q. Prove that in two concentric circle, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.

3.88

, circles with centers

X

Y

touch internally at point

Z

S e g B Z

is a chord of bigger circle and it intersect smaller circle at point

A

s e g A X | | s e g B Y

Q. Two circles touch each other internally at a point

P

A B

of the bigger circle intersects the other circle in

C

D

∠ C P A = ∠ D P B

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