Number of tangents from a point MCQs

Q1. A quadrilateral ABCD circumscribes a circle. If AB = 4, BC = 5 and CD = 3 cm, then AD is:

• A.2
• B.5
• C.1
• D.7

Answer: A. 2

Q2. ABCD has an inscribed circle. Given AB = 4, BC = 5, CD = 4 cm, find AD:

• A.8
• B.3
• C.5
• D.0

Answer: B. 3

Given 4 cm, asked for find AD. By hence the answer = 3. hence the answer = 3. draw the relevant radii and use the fact that the tangent _|_ radius at the contact point. Putting it together option B) 3. Others fail: option A) '8' is wrong because Wrong: uses an incorrect intermediate value; option C) '5' is incorrect: Wrong: a step was skipped or HCF/LCM swapped.

Q3. A quadrilateral ABCD circumscribes a circle. If AB = 4, BC = 5 and CD = 7 cm, then AD is:

• A.11
• B.6
• C.5
• D.-3

Answer: B. 6

First, read what's there - a typical math numerical. The data on the table: 7 cm. We are after the quantity the stem asks for. Tool of choice - hence the answer = 6. Rearrange it for the unknown before substituting. Numbers in: hence the answer = 6. Common-sense check: draw the relevant radii and use the fact that the tangent _|_ radius at the contact point. Lock in option B) 6. Trap-watch: option A) '11' is incorrect: Wrong: uses an incorrect intermediate value; option C) '5' fails since Wrong: a step was skipped or HCF/LCM swapped.