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  • Q1.Two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that angleAPB = 2 angleOAB. Q2. In a circle of radius 17 cm , two parallel chords are drawn on opposide sides of diameter.The distance between two chords is 23 c

Q1.Two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that angleAPB = 2 angleOAB. Q2. In a circle of radius 17 cm , two parallel chords are drawn on opposide sides of diameter.The distance between two chords is 23 cm and length of one chord is 16 cm , then the lenth of the other chord is.....

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1);Let;angle OAB=x\* ecause OA=OB Rightarrow angle OAB= angle OBA=x\* herefore angle OAP=angle OBP=90^circ;;;;;;;;(tangent;to; circle)\* herefore angle BAP=angle ABP=90^circ-x\* Now,;In riangle APB,\* Rightarrow angle APB+angle ABP+angle PAB=180^circ\* Rightarrow angle APB+ 90^circ-x+90^circ-x=180^circ\*Rightarrow angle APB=2x,;Hence;proved\* 2);We;know;that;perpendicular;from;the;centre;of;circle;bisects;the;chord\* Rightarrow FD=8;cm\* OD=DB=r=17;cm\* Let;OF=x Rightarrow OE=23-x\*In; riangle OFD\* OD^2=OF^2+FD^2\* Rightarrow 289=x^2+64Rightarrow x=15\* Rightarrow OE=23-15=8;cm \* Now,;In; riangle OEB\* OB^2=OE^2+EB^2\* Rightarrow 289=64+ y^2\* Rightarrow y=15\* herefore Length;of;chord;AB=2y=30;cm\*

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Deependra Verma

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