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If the radius of the circum-circle of an isosceles triangles ABC is equal to AB (= AC), then angle A is :

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In `DeltaP Q R`,the radius of the circumcircle is given by
`(PQ)/(2sinR)=(QR)/(2sinP)=(PR)/(2sinQ)`
But, it is given that the radius is PQ (=PR).
`thereforePQ=(PQ)/(2sinR)`
`rArrsinR=1/2angleR=(pi)/6`
But, PQ=PR
`rArrangleR=angleQrArrangleQ=angleR=pi/6`
`thereforeangleP=pi-angleR-angleQ=(2pi)/3`
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OBJECTIVE RD SHARMA ENGLISH-PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM-Chapter Test
  1. If the radius of the circum-circle of an isosceles triangles ABC is eq...

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  2. If the sides of a triangle are in the ratio 3 : 7 : 8, then find R : r

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  3. The area of a regular polygon of n sides is (where r is inradius, R is...

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  4. If the angles of a triangle are 30^(@) and 45^(@), and the included si...

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  5. In a DeltaABC, angleB=(pi)/(3) and angleC=(pi)/(4) let D divide BC in...

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  6. If A is the area and 2s is the sum of the sides of a triangle, then Al...

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  7. If in a triangle ABC, right angled at B, s-a=3, s-c=2, then the values...

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  8. If the sides of a triangle are a, b and sqrt(a^(2) + ab + b^(2)), then...

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  9. In a DeltaA B Csum(b+c)tanA/2tan((B-C)/2)=

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  10. In triangle ABC, angleA=pi/3 and b:c =2:3, tan theta=sqrt3/5, 0 lt the...

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  11. In a DeltaABC, AD is the altitude from A. Given b gt c, angleC=23^(@)"...

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  12. If the angles A, B, C (in that order) of triangle ABC are in arithmeti...

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  13. If the radius of the incircle of a triangle withits sides 5k, 6k and 5...

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  14. Two sides of a triangle are 2sqrt2 and 2sqrt3cm and the angle opposite...

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  15. In a triangleABC, a=13cm, b=12 and c=5cm The distance of A from BC is

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  16. In a triangleABC,B=pi/8, C=(5pi)/(8). The altitude from A to the side ...

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  17. In DeltaABC, A = (2pi)/(3), b -c = 3 sqrt3 cm and " area of " Delta AB...

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  18. In DeltaABC if a=(b-c)sectheta then (2sqrt(bc))/(b-c)sin(A/2)=

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  19. In a DeltaABC, (a + b + c) (b + c - a) = lambda bc. (where symbols ha...

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  20. If in DeltaABC, a=2b and A=3B, then A is equal to

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  21. Let the angles A , Ba n dC of triangle A B C be in AdotPdot and let b ...

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