Q16 of 31 Page 65

The centre of two concentric circle is O; a straight line intersects a circle at the points A and B and other circle at the points C and D. If AC = 5 cm. then the length of BD is


In OAP and OBP


⇒ AP = BP


⇒ OA = OB


⇒ OP = OP


In OCP and ODP


⇒ CP = DP


⇒ CA + AP = BP + DB


⇒ CA = DB + BP-AP


⇒ CA = DB + 0


⇒ CA = DB


So, BD = 5cm

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Let us write True/False:

i. Only one circle can be drawn through three collinear points


ii. The two circles ABCDA and ABCEA are same circle.


iii. If two chord AB and AC of a circle with its centre O are situated on the Opposite side of the radius OA, then ∠OAB=∠OAC.

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Let us fill in the blanks:

i. If the ratio of two chords PQ and RS of a circle with its centre O is 1 : 1, then ∠POQ: ∠ROS=_______________


ii. The perpendicular bisector of any chord of a circle is __________ of that circle.