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Point S lies in the interior of A PQR. P...

Point S lies in the interior of A PQR. Prove that, SQ + SR `lt` PQ + PR.

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Point S lies in the exterior of a circle with centre P and radius 33cm. A tangent from S touches the circle at T and ST=56cm. Find the distance of S from P.

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In triangleABC , point D lies on side BC. E is the midpoint of AD. Prove that, ar(EBC)= 1/2 ar(ABC)

The diagonal AC of a parallelogram ABCD intersects DP at the point Q, where ‘P’ is any point on side AB. Prove that CQ xx PQ = QA xx QD .

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In the given figure, PR gt PQ and PS bisects angle QPR. Prove that angle PSR gt angle PSQ .

ABCD is a parallelogram. AC and BD are the diagonals intersect at O. P and Q are the points of tri section of the diagonal BD. Prove that CQ" ||" AP and also AC bisects PQ (see figure).

In adjacent figure, PR > PQ and PS bisects /_QPR . Prove that /_PSR > /_PSQ .

If the normals at P, Q, R of the parabola y^2=4ax meet in A and S be its focus, then prove that .SP . SQ . SR = a . (SA)^2 .

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KUMAR PRAKASHAN-TRIANGLES-SKILL TESTING EXERCISE
  1. In the given figure, XM and YN are both lt perpendicular to line segme...

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  2. In the given figure AB and CD bisect each other at O. Prove that AC = ...

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  3. In rectangle ABCD, E is the midpoint of side BC. Prove that, AE = DE.

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  4. Prove that the medians of an equilateral triangle are equal.

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  5. In the given figure, AB and DC are both perpendicular to line segment ...

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  6. In triangle ABC, AB = AC and the bisector of angle A lt intersects BC ...

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  7. In triangle ABC, the bisectors of angleB and angle C intersect at I. ...

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  8. In triangle ABC, AB = AC and angle A = 36^(@). The bisector of angle C...

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  9. In the given figure, PS = PR and angle TPS = angle QPR. Prove that P...

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  10. In triangle ABC, D is the midpoint of BC. DFZAB and DE bot AC, where p...

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  11. In parallelogram ABCD, diagonals AC and BD are equal. Find the measure...

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  12. triangle ABC and triangle DBC are isosceles triangles on the same base...

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  13. AD, BE and CF are altitudes of triangle ABC. If AD = BE = CF, prove t...

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  14. In quadrilateral ABCD, BA = BC and DA = DC. Prove that BD bisects ang...

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  15. In triangle ABC, AB gt AC and D is any point of BC. Prove that, AB gt...

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  16. In triangle ABC, AC gt AB. AB is extended to P and AC is extended to Q...

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  17. In triangle ABC, AD, BE and CF are altitudes. Prove I, that, AD + BE +...

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  18. Point S lies in the interior of A PQR. Prove that, SQ + SR lt PQ + PR.

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  19. In triangle ABC, AD is a median. Prove that AB + AC gt 2AD

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  20. For any triangle, prove that the sum of the sides of the triangle is g...

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