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In Fig. 10.19, the incircle of A B C...

In Fig. 10.19, the incircle of ` A B C` touches the sides `B C ,\ C A` and `A B\ a t\ D ,\ E` and `F` respectively. Show that `A F+B D+C E=A E+B F+C D=1/2(P e r i m e t e r\ of\ A B C)` (FIGURE)

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RD SHARMA-CIRCLES-All Questions
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  2. A circle is touching the side B C of A B C at P and touching A ...

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  3. In Fig. 10.19, the incircle of A B C touches the sides B C ,\ C...

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  4. In Fig. 10.20, the sides A B ,\ B C and C A of triangle A B C touc...

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  5. In Fig. 10.21, two circles touch each other at the point C . Prove ...

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  6. A circle touches all the four sides of a quadrilateral A B C D . Pr...

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  7. If all the side of a parallelogram touch a circle, show that the pa...

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  8. The radius of the incircle of a triangle is 4 cm and the segments i...

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  9. Prove that the tangents at the extremities of any chord make equal ...

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  10. Two tangents T P and T Q are drawn to a circle with centre O fro...

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  11. P Q is a chord of length 8 cm of a circle of radius 5 cm. The tange...

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  12. In Fig. 10.32, l and m are two parallel tangents at A and B . Th...

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  13. Prove that the angle between two tangents drawn from an external po...

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  14. Show that tangent lines at the end points of a diameter of a circle...

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  15. Two concentric circles are of radii 5 cm and 3 cm. Find the length ...

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  16. A circle touches the sides of a quadrilateral A B C D at P ,\ Q ,\ ...

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  17. Find the locus of the centres of circles which touch a given line a...

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  18. Find the locus of centres of circles which touch two intersecting l...

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  19. If P T is a tangent at T to a circle whose centre is O and O P=1...

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  20. Find the length of a tangent drawn to a circle with radius 5 cm, fr...

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