In a triangle ABC, AB + BC = 12 cm, BC + CA = 14 cm and CA + AB = 18 cm. Find the radius of the circle (in cm) which has the same perimeter as the triangle
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ABC is an isosceles triangle such that AB = AC and ∠B = 35°, AD is the median to the base BC. Then ∠BAD is
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In a triangle ABC, AB = AC, ∠BAC = 40° then the external angle at B is :
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In ΔABC ∠A = 90° and AD ⊥ BC where D lies on BC. If BC = 8 cm, AD = 6 cm, then arΔABC : arΔACD = ?
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The angle between the external bisectors of two angles of a triangle is 60°. Then the third angle of the triangle is
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In ΔABC, D and E are points on AB and AC respectively such that DE || BC and DE divides the ΔABC into two parts of equal areas. Then ratio of AD and BD is
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ABC is an isosceles triangle with AB = AC, A circle through B touching AC at the middle point intersects AB at P. Then AP : AB is:
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Taking any three of the line segments out of segments of length 2 cm, 3 cm, 5 cm and 6 cm, the number of triangles that can be formed is:
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If the median drawn on the base of a triangle is half of its base the triangle will be
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I is the incentre of ΔABC. If ∠ABC = 60°, ∠BCA = 80°, then the ∠BIC is
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In a triangle, if three altitudes are equal, then the triangle is
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In an isosceles triangle, if the unequal angle is twice the sum of the equal angles, then each equal angle is
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If the length of the sides of a triangle are in the ratio 4 : 5 : 6 and the inradius of the triangle is 3 cm, then the altitude of the triangle corresponding to the largest side as base is :
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In a right-angle ΔABC, ∠ABC = 90°, AB = 5 cm and BC = 12 cm. The radius of the circumcircle of the triangle ABC is
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In triangle PQR, points A, B and C are taken on PQ, PR and QR respectively such that QC = AC and CR = CB. If ∠QPR = 40°, then ∠ACB is equal to:
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If ABC is an equilateral triangle and D is a point of BC such that AD ⊥ BC, then
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ΔABC is an isosceles triangle and = = 2a unit, = a unit. Draw ⊥ , and find the length of
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ABC is a triangle. The bisectors of the internal angle ∠B and external angle ∠C intersect at D. If ∠BDC = 50°, then ∠A is
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AD is the median of a triangle ABC and O is the centroid such that AO = 10 cm. The length of OD (in cm) is
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The side QR of an equilateral triangle PQR is produced to the point S in such a way that QR = RS and P is joined to S. Then the measure of ∠PSR is
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