In circle O, if LP congruent LK, find the measurement of the major arc PNK. A. 112 B.156 C.224 D.248
2 answers:
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Answer:
Step-by-step explanation:
1. You must apply the following formula for calculate the total surface area the regular pyramid:
Where p is the perimeter of the base, l is the slant height and B is the area of the base.
2. The perimeter is, where s is the side length:
3. The faces are isosceles traingles. So, to find the slant height you can divide one base into two equal right triangles and calculate the slant height with Pythagorean Theorem:
4. The base is equal to any face, then both have equal areas. As previously you divide one base into two equal righ triangle to find the slant height, you can calcualte the area of one right triangle and multply it by 2 to calculate B:
Finally substitute values:
Answer:
Step-by-step explanation:
Given: △ABC, BC>AC, D∈ AC , CD=CB
To prove: m∠ABD is acute
Proof: In ΔABC, the angle opposite to side BC is ∠BAC and the angle opposite to side AC is ∠ABC.
Now, it is given that BC>AC, then ∠BAC>∠ABC.. (1)
In ΔBDC, using the exterior angle property,
∠ADB=∠DBC+∠BCD
∠ADB=∠DBC+∠BCA
⇒∠ADB>∠BAC (2)
From equation (1) and (2), we get
∠ADB>∠BAC
⇒∠ADB>∠ABC
⇒DB>AB
Hence, m∠ABD is acute
