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The circumcentre, incentre, orthocentre ...

The circumcentre, incentre, orthocentre and the centroid of a triangle are one and the same point. The triangle must be:
एक त्रिभुज के परिकेंद्र, अंतःकेंद्र, लम्ब केंद्र तथा केंद्रक एक ही हैं तथा समान बिंदु हैं | यह त्रिभुज अवश्य होगा -

A

Isosceles/ समद्विबाह

B

right-angled/ समकोण

C

right-angled isosceles/ समकोण समद्विबाहु

D

equilateral/ समबाहु

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O,G,I and H are respectively the circumcentre, centroid, incentre and orthocentre of an equilateral triangle. Which of these points are identical ? / O, G, I तथा H क्रमशः एक समबाह त्रिभुज के परिकेंद्र, केंद्रक, अंतःकेंद्र और लम्बकेंद्र हैं | निम्न में से कौन से बिंदु समसरूप हैं ?

The sides of a triangle are in the ratio 3 : 2 : 4 and the perimeter is 72 cm, The sides are: एक त्रिभुज की भुजाएं 3 : 2 : 4 के अनुपात में हैं तथा इसका परिमाप 72 सेमी है | भुजाएं ज्ञात करें |

ABC is an equilateral triangle. P,Q and R are the midpoints of sides AB, BC and CA respectively. If the length of the side of the triangle ABC is 8 cm, then the area of triangle PQR is: ABC एक समबाहु त्रिभुज है | P, Q और R क्रमशः भुजाओं AB, BC तथा CA के मध्य बिंदु हैं | यदि त्रिभुज ABC की भुजा की लंबाई 8 सेमी है, तो त्रिभुज PQR का क्षेत्रफल कितना होगा ?

O, G, I and H are respectively the circumcenter, centroid, incentre and orthocentre of an equilateral triangle. which of these points are identical? किसी समबाहु त्रिभज में O, G, I और H क्रमशः परिकेद्र(circumcentre), केंद्रिका (centroid),अंत:केंद्र(incentre)और लंबकेंद्र (orthocentre) है| इनमें से कौन से बिंदु एक समान हैं?

The in-radius of a triangle is 6 cm, and the sum of the length of its sides is 50cm. The area of the triangle (in sq. cm) is एक त्रिभुज को अंतः त्रिज्या 6 सेमी है, तथा इसके भुजाओं के लंबाई का योग 50 सेमी है। त्रिभुज का क्षेत्रफल (वर्ग सेमी में) ज्ञात करें।

The sides of a triangle are 16 cm, 30 cm and 34 cm respectively. At each vertices, circles of radius 7 cm are drawn. What is the area of the triangle, excluding the portion covered by the sectors of the triangle? ( pi=22/7 ) एक त्रिभुज की भुजाएं क्रमशः 16 सेमी, 30 सेमी तथा 34 सेमी की हैं | प्रत्येक शीर्ष पर 7 सेमी त्रिज्या वाले वृत्त खींचे जाते हैं | वृत्त के खंडो द्वारा घेरे गए भाग को छोड़ कर त्रिभुज का क्षेत्रफल ज्ञात करें |

The vertices of triangle PQR lie on a circle with centre O. SR is a tangent to the circle at the point R. If QR bisects the angle ORS , then what is the measure of angle RPQ ? त्रिभुज PQR के शीर्ष बिंदु एक वृत्त पर अवस्थित हैं जिसका केंद्र O है| SR बिंदु R पर वृत्त की स्पर्श रेखा है | यदि QR, angle ORS को द्विभाजित करता है, तो कोण RPQ का माप ज्ञात करें |

The sides of a triangle are in the ratio 3 : 4 : 5. If the perimeter of the triangle is 24 cm, its area is: एक त्रिभुज की भुजाएं 3 : 4 : 5 के अनुपात में हैं | यदि इस त्रिभुज का परिमाप 24 सेमी है, तो इसका क्षेत्रफल ज्ञात करें |

PINNACLE-GEOMETRY-EXERCISE
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  2. PA and PB are the tangents to a circle with centre O, from a point P o...

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  7. In a triangle ABC, AD is perpendicular to BC from A, if angle BAC = 90...

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  9. It is given that the area of a triangle is A. The values of its perime...

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  10. The area of a sector of a circle with central angle 60^@ is A. The ci...

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  11. It is given that triangle ABC ~ triangle PRQ and that Area ABC : Area ...

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  12. O,G,I and H are respectively the circumcentre, centroid, incentre and ...

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  13. triangle ABC ~ triangle DEF and their perimeters are 64 cm and 48 cm ...

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  14. AB and CD are two chords of a circle which intersect at a point O insi...

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  15. The perimeter of triangle ABC is 24 cm and its side, BC =9 cm. AD is t...

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