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4vir4ik [10]
3 years ago
6

O is the centre of the circle and ABC and EDC are tangents to the circle. Find the size of angle BCD. You must give reasons in y

our answers.

Mathematics
1 answer:
Simora [160]3 years ago
7 0

Answer:

mBCD = 28°

Step-by-step explanation:

The angle mBFD inscribes the arc mBD, so we have that:

mBFD = mBD/2

76 = mBD/2

mBD = 152°

The angle mBOD is a central angle related to the arc mBD, so we have that:

mBOD = mBD = 152°

In the quadrilateral BODC, the sum of internal angles needs to be equal to 360° (property of all convex quadrilaterals). The angles mCBO and mCDO are right angles, because EDC and ABC are tangents to the circle.

So, we have that:

mBOD + mCDO + mBCD + mCBO = 360

152 + 90 + mBCD + 90 = 360

mBCD = 360 - 90 - 90 - 152

mBCD = 28°

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Answer:

P = (65 - R) / 60

Step-by-step explanation:

Raul's grandfather is Miguel

Raul's sister is Paula

We are given that Raul’s age is the same as his grandfather’s age minus 60 times the age of his sister. If we write this mathematically, we have that:

R = M - (60*P)

Where R = Raul's age, M = Miguel's age and P = Paula's age

We are then given that Miguel is 65 years old, this means that M = 65

=> R = 65 - 60P

To find Paula's age, we make P the subject of formula, hence:

60P = 65 - R

=> P = (65 - R) / 60

We can use this expression to find Paula's age.

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