Q4 of 100 Page 17

In Fig. 16.196, if ∠AOB = 80° and ∠ABC=30°, then find ∠CAO.

2 ∠OAB = 100°

∠OAB = 50°


Therefore,


∠OAB = ∠OBA = 50°


∠AOB = 2 ∠BCA (Angle subtended by any point on circle)


80° = 2 ∠BCA


∠BCA = 40°


Now,


In triangle ABC


∠A + ∠B + ∠C = 180°


∠A + 30o + 40o = 180°


∠A = 110°


∠CAB = ∠CAO + ∠OAB


110° = ∠CAO + 50°


∠CAO = 60°


More from this chapter

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2

In Fig. 16.194, two congruent circles with centres O and O’ intersect at A and B. If ∠AO’B=50°, then find ∠APB.

 3

In Fig. 16.195, ABCD is a cyclic quadrilateral in which ∠BAD=75°, ∠ABD=58° and ∠ADC=77°, AC and BD intersect at P. Then, find ∠DPC.

 5

In Fig. 16.196, if O is the circumcentre of Δ ABC, then find the value of ∠OBC + ∠BAC.

 6

In Fig. 16.197, AOC is a diameter if the circle and arc AXB=arc BYC. Find ∠BOC.