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Circles C(O, r) and C(O', r'), (r gt r')...

Circles C(O, r) and C(O', r'), `(r gt r') ` touch internally at P. PQ is a chord of circle C(O, r) which intersects C(O', r') at R. Show that OO'RQ is a trapezium

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Angle included between the chord and tangent of a circle is equal to the angle in alternate segment
Also, the angle subtended by the chord at center is twice the angle in the segment of same chord
`:./_PO’R =/_POQ`
But these angles are corresponding angles
`:. OQ||O’R`
As well as QR is not parallel to OO’ (they are two distinct line having common vertex P)
Hence, quadrilateral OO’RQ is a trapezium
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